Paul Pogba created one goal and scored another as Juventus finally claimed their first Serie A win of the season, while Francesco Totti hit his 300th goal for Roma in a 2-2 draw with Sassuolo.
After their worst start to the season in several decades, Juventus travelled to Genoa hoping to build on an impressive 2-1 Champions League victory over Manchester City in midweek.
Pogba helped break the deadlock in the 37th minute when he got on the end of Roberto Pereyra's cross at the back post to fire a volley off the bar and into the net after the ball bounced off goalkeeper Eugenio Lamanna.
Juventus were given a boost when Armando Izzo saw red on the stroke of half-time after being cautioned for a second time when he pulled Juan Cuadrado to the ground.
But it took a penalty decision to see Juventus ease towards safety, Pogba stepping up to beat Lamanna on the hour after defender Giorgio Chiellini had been impeded by Diogo Figueiras.
Juve's first league win of the season came at the fourth attempt but the champions are still eight points adrift of early pacesetters Inter, who had Mauro Icardi's first-half winner -- the Argentinian's first goal of the season -- to thank for a patchy 1-0 win at Chievo.
Inter will remain top for at least another week, with a two-point cushion on Torino, who saw Juventus reject Fabio Quagliarella hit the net twice in a precious 2-0 home win over hapless Sampdoria.
Roma are third, a further point adrift after a frustrating display by Rudi Garcia's scudetto challengers only days after they battled to a commendable 1-1 Champions League draw with defending champions Barcelona.
Garcia rested several first team regulars with Edin Dzeko notably starting on the bench in favour of Totti, who on Sunday started in the league for the first time this season.
Perhaps aware of Roma's fatigue from their extra midweek exertions, Sassuolo made a lightning start and Gregoire Defrel flashed just wide of Morgan De Sanctis's post from a corner on the quarter hour.
Defrel's pace was causing problems and minutes later the Frenchman stunned the hosts with a fine daisycutter from 25 metres that left De Sanctis rooted to the spot.
Roma pulled level shortly after, although a suspicion of offside accompanied Totti's goal after he latched on to Miralem Pjanic's midfield pass to beat Andrea Consigli with a bobbling shot from the edge of the area.
It was far from spectacular, but the goal took Totti's tally to 300 in all competitions for the club for whom he made his debut in March 1993.
Totti almost turned provider minutes later, setting Mohamed Salah up with a delightful chip inside the area only for the Egyptian to drag his shot wide of the far post.
The miss proved costly, Sassuolo restoring their lead on the stroke of half-time when Matteo Politano beat De Sanctis with an angled drive the 'keeper really should have saved.
Salah pulled Roma level with his maiden league goal for the club four minutes after the restart, but afterwards Roma had little to offer.
Salah produced a great curling effort a minute from the final whistle that looked to be heading for the top corner until Consigli produced a fine save to secure a share of the spoils.
Later Sunday, Fiorentina and Lazio will look to climb up to third place when they travel to Carpi and Napoli respectively.