Anthony Martial, bidding to become the first United player since Ian Storey-Moore in 1972 to score on his first three league appearances for the club, was kept quiet.
Rooney, meanwhile, who had not scored a league goal in 11 matches stretching back to early April, again looked short of his best.
It was left to the midfielders to try and unlock Sunderland's defence, with Mata sending a deflected shot just wide and Depay forcing former City goalkeeper Costel Pantilimon to palm a long-range shot over the bar.
Pantilimon was earlier penalised for handling outside the penalty area, but Mata wasted the free-kick.
For all United's dominance, Sunderland did manage periods of relief on the break, Jeremain Lens forcing David de Gea to save an angled drive with his feet from the visitors' best chance of the first half.
But just as it looked as though they would get to half-time unscathed, Sunderland fell behind with almost the final touch of the first half.
Daley Blind floated an angled ball over the visitors' defence for Mata to square to Depay, who tapped in from close range to claim his first domestic goal since joining United from PSV Eindhoven.
If that was bad news for Sunderland, what happened 30 seconds into the second half was a disaster as the game was taken beyond them.
Again Mata was involved with a pass to Martial, who showed great strength to reach the byline and drive in a low cross that Rooney forced into the net from close range with his knee.
After Sunderland had seen chances of an unlikely comeback snuffed out as De Gea saved from Ola Toivonen and Patrick van Aanholt, Depay should have made it 3-0 from Martial's pass, but failed to beat Pantilimon.
Pantilimon also saved well from Mata 10 minutes from the end, but he was powerless to prevent the Spaniard firing past him from an Ashley Young cross to cap a red-letter day for United.