Hodgson gave a debut to Southampton left-back Luke Shaw and experimented with a malleable new playing system, but it took the second-half introductions of Adam Lallana and Danny Welbeck to give England a spark.
Lallana teed up the winning goal for Sturridge, whose back-post header ended a 264-minute goal drought for England at Wembley Stadium after November's friendly defeats by Chile and Germany.
It was a night that left Hodgson with as many questions as answers, but when his side next take to the field at Wembley against Peru on May 30, he will have already selected his squad for the trip to Brazil.
"It was a very organised Danish team and we had to work very hard," said Hodgson.
"(Denmark goalkeeper) Kasper Schmeichel had an outstanding game in goal. From the 60th minute onwards we showed some really good play and Adam Lallana made a big difference."
While English thoughts are fully fixed on the World Cup, the evening began with a nod to the past, as the deaths of England greats Tom Finney and Bert Williams, as well as former Denmark manager Richard Moller Nielsen, were marked with a minute's applause.
Hodgson included five Liverpool players in his starting XI and there was a fluidity to England's shape that seemed designed to recreate the Merseyside club's approach under their current manager, Brendan Rodgers.
Wayne Rooney swapped positions with the Liverpool pair of Sturridge and Raheem Sterling, with a chipped pass from the latter allowing the Manchester United man to elude Denmark goalkeeper Kasper Schmeichel, only to lash well wide of the vacant goal.
Denmark created two clear chances in the first half, with Michael Krohn-Dehli volleying over from a Casper Sloth cross and Chris Smalling obliged to block after Jakob Poulsen was allowed to bear down on goal.
It was England, however, who came closest to opening the scoring, with Sterling hitting the post from Ashley Cole's low cross before Schmeichel channelled the inspiration of his illustrious father, Peter, by spreading himself brilliantly to save at the feet of Sturridge.
Shaw was handed his debut at half-time, the 18-year-old coming on as a substitute for Cole and becoming the fourth Southampton player to be awarded a first cap by Hodgson.
He quickly caught the eye, striding forward and whipping in a dangerous cross, but Denmark continued to threaten, with Joe Hart saving from Nicklas Bendtner and then flying out to thwart substitute Morten Rasmussen.
The introductions of Lallana and Welbeck gave England extra invention in attack though, and the hosts belatedly began to apply concerted pressure.
Welbeck twice forced Schmeichel into action with a crisp drive and then a poked shot from Jordan Henderson's pass, before the Leicester City goalkeeper had to tip over a rasping effort from Sturridge.
With eight minutes remaining the pressure told, as Sturridge headed Lallana's clipped left-wing cross past Schmeichel to give England hope of more convincing displays ahead.
The best Denmark could offer in response was a half-volley from Danny Olsen that comfortably cleared Hart's crossbar, but although Morten Olsen's side will not play at the World Cup, they were far from outclassed.
"It's not the way we wanted to play, but it's the game we had to play at the moment," said the visiting coach, many of whose players have only recently returned to action after Denmark's domestic winter break.
"I'm satisfied with the way we defended, but it's not the way we want to play football. We want to have the ball, but we don't have the power for the moment."
This midweek's round of international friendly fixtures constitutes a last chance for many players to force their way into the reckoning ahead of the World Cup in Brazil in June and July.
Wedged into a busy period in the club season, 99 days before the World Cup itself begins, it is the only international date before most coaches announce their squads for the finals in May. Uncapped teenage full-back Luke Shaw will be the freshest face in the England squad for a friendly against Denmark at Wembley in which Liverpool right-back Glen Johnson will win his 50th cap.
England manager Roy Hodgson - who revealed on Tuesday that his players will work with a sports psychiatrist in the build-up to the World Cup - insisted that the 30-man group he named for the game is "not a definitive squad" as he prepares to send his provisional World Cup list to FIFA by May 13. But it is England's only game before then and captain Steven Gerrard had a message for those on the fringes of the squad.
"It is time to start getting excited," said the Liverpool midfielder. (The World Cup) will be here before we know it. It is time as a player you want to continue to impress the manager or grasp your opportunity to impress."
England are preparing for the start of their World Cup campaign against Italy in Manaus, so they will be keeping a keen eye on the Azzurri's friendly clash with Spain in Madrid.
The game at Atletico Madrid's Vicente Calderon stadium is a repeat of the Euro 2012 final, which La Roja won 4-0 in Kiev, and it is also set to see Atletico's Brazilian-born striker Diego Costa make his Spain debut. Costa, 25, has scored 21 times in La Liga this season and Spain had to battle with the Brazilian Confederation to get him on board.
Barcelona left-back Jordi Alba said on Tuesday that Costa, who first arrived in Spain in 2007, has been warmly welcomed into the squad. "We have received him with open arms, he is a player that I love. For the rest of the team it is incredible that he is here," he said.
While Costa comes in, coach Vicente del Bosque has notably left David Villa, Fernando Torres and Juan Mata out of a squad that continues to evolve ahead of their World Cup defense. Spain's opening World Cup test will be against the team they beat in the 2010 final, the Netherlands, in Salvador, and the Dutch continue their preparations with a heavyweight friendly of their own, away to France.
Dutch coach Louis van Gaal, who looks set to be replaced by Guus Hiddink after the summer, will give chances to youngsters and there are some new faces in the France squad too, such as Real Sociedad forward Antoine Griezmann, scorer of 15 goals in La Liga this season.
Coach Didier Deschamps, who will be overseeing France's first game since the dramatic play-off win against Ukraine in November that took them to the World Cup, has however cast doubt over whether Griezmann will be on the plane to Brazil.
"I am convinced that he has great potential but I can't say for certain about anybody yet, There is an apprenticeship phase and two or three games is not enough." he said.
World Cup hosts Brazil cross the Atlantic for a meeting with South Africa in Johannesburg, where coach Luiz Felipe Scolari expects a tough test against a side who beat Spain in November, and Germany entertain Chile in Stuttgart with coach Joachim Loew admitting to concerns about the form and fitness of his bigger names.
"I appeal to all of the squad to prepare their case as strongly as possible, just as it needs to be if they have big goals in mind," said Loew.
Chile's pedigree cannot be doubted, and Jorge Sampaoli's team beat England 2-0 on their last trip to Europe in November.
Among other games, Romania host Argentina in Bucharest, while the United States face Ukraine in a match that will be held in Cyprus due to the current political tension in Kiev.
England manager Roy Hodgson will run the rule over his players for the last time before naming his World Cup squad when they tackle Denmark in a friendly on Wednesday.
Hodgson will not announce his 23-man selection and seven standby players for the World Cup until May 13, but the match at Wembley Stadium represents his final opportunity for experimentation before he does so.
Having seen his side lose at home to Chile and Germany in friendly games last November, Hodgson is seeking to avoid becoming the first England manager ever to lose three consecutive fixtures on home soil. However, with the World Cup in Brazil looming on the horizon, he has hinted that he may use Denmark's visit to examine some of the players on the fringes of his first nine.
"The Denmark game is very much a game where I've got to think about what experimentations I need," he said.
"If we take Steven Gerrard, does he need to play against Denmark to prove to me that he needs to play against Italy?
Would I be better off playing somebody else because I know what Steven Gerrard can do? He's got 103 caps. Could (Wayne) Rooney be in the same category as Gerrard? And Joe Hart too?"
The 30-man squad that Hodgson announced for the game did not contain any major surprises, but Southampton left-back Luke Shaw was awarded a first senior call-up. The 18-year-old has both Leighton Baines and Ashley Cole ahead of him in the pecking order, but Cole's lack of playing time at Chelsea may hand Shaw an opportunity to gazump him. On the opposite side of the defence, a hip injury to Tottenham Hotspur's Kyle Walker means that Liverpool's Glen Johnson is likely to win his 50th cap at right-back, while Everton centre-back Phil Jagielka is also absent.
Another player hoping to catch Hodgson's eye is Arsenal midfielder Alex Oxlade-Chamberlain, who has impressed in recent weeks after missing the first half of the season with a knee problem.
"I think you always have to be on your toes and make sure that when you have opportunities to play for your club or country, you take it and show what you have to offer, I don't think I'm playing catch-up (in terms of fitness). I'm a young player and I'm still learning. When I get the opportunity, I always try to do my best."said the 20-year-old.
Having missed out on a place at the World Cup, Denmark will use the game to begin preparations for their Euro 2016 qualifying campaign. Morten Olsen's side finished six points adrift of Italy in World Cup qualifying and face a difficult task to reach Euro 2016, having been drawn alongside Portugal and Serbia in Group I.
Denmark must do without Tottenham playmaker Christian Eriksen and Toulouse forward Martin Braithwaite due to injury, which prompted Olsen to draft Jakob Ankersen, Jakob Poulsen and Simon Makienok into his squad.
With the Danish Superliga season having only just resumed after its winter break and most of Denmark's players plying their trade in their homeland, Olsen concedes that England will have a physical advantage.
"The English players are in fantastic match condition, while some of our players can't have the same level of match fitness as we have only recently resumed our domestic league, So this will be quite a match for them. We will need to perform as a team if we are to stand a chance against them at Wembley." he said.
Denmark's players will wear black armbands in tribute to Richard Moller Nielsen, coach of the team that pulled off a shock triumph at Euro 92, following his death last month at the age of 76.
Moller Nielsen, who was 76, had been diagnosed with a brain tumor in June last year and later underwent surgery. Denmark's victory in Sweden in 1992 was a triumph of fairytale proportions as the team had not even qualified for the finals and the players were preparing for their summer holidays.
But the former Yugoslavia, torn apart by civil war, were thrown out of the competition by European football's governing body UEFA and Denmark were told to take their places at the last minute.
And, with a team crammed full of talent including goalkeeper Peter Schmeichel, midfielder John Jensen and strikers Henrik Larsen and Fleming Povlsen, they defied the odds and beat the Netherlands in the semi-final before a memorable 2-0 win over then World Cup holders Germany in Gothenburg in the final.
Former Manchester United goalkeeper Schmeichel led the tributes to Moller Nielsen. He posted on Twitter: "Richard Moller Nielsen, an inspiration, my teacher and my friend. R.I.P my friend." Moller Nielsen later managed the Finland and Israel national teams.