Victory was especially sweet for United as Sunderland’s fans had celebrated exuberantly at the Stadium of Light on the final day of last season when United found out they had been pipped to the title by City.
“They weren’t the only fans who enjoyed that, but that’s gone now,” United midfielder Michael Carrick told Sky Sports. “It was about coming here, getting the points, ticking the game off and keeping the run going.”
Defeat left Sunderland four points above the relegation zone in 16th place, although they have played at least a game more than the teams immediately below them.
Elsewhere on Saturday, an 81st-minute goal from Arouna Kone gave Wigan Athletic a 1-0 win at home to Norwich City which hauled Roberto Martinez’s side out of the relegation zone at Aston Villa’s expense.
Meanwhile, Andy Carroll scored twice, with Gary O’Neil also on target, as West Ham United eased their own relegation fears by beating West Bromwich Albion 3-1.