United had dominated the game but it took them 66 minutes to make the breakthrough, Wayne Rooney scoring from the penalty spot.
Radamel Falcao won it with a superb piece of skill in the box, and when John O???Shea brought him down, referee Roger East gave the penalty – correctly – but inexplicably sent Wes Brown off.
Rooney grabbed the second on 84 when Adnan Januzaj???s shot was parried by Costel Pantilimon and the United captain buried the rebound.
Sunderland???s poor run continues ??? just one win in 10 matches now for Gus Poyet???s men.
Southampton missed the chance to move into fourth place as they went down 1-0 at West Brom.
Saido Berahino scored a superb goal just two minutes in, but Saints ??? and in particular Graziano Pelle ??? will be kicking themselves that they did not at least take a point back down to the south coast.
Pelle contrived to miss the ball from a yard out from Ryan Bertrand???s second-half cross, as the Italian striker???s woeful form in 2015 continues. That???s three games without a win now for Southampton.
Burnley remain in deep trouble after going down 1-0 at home to Swansea. The Swans built on last week???s fine win over Manchester United with another three points, though the goal ??? on 64 minutes – will not be on the Goals of the Season shortlist.
A corner was headed on by Bafetimbi Gomis, and in the ensuing scramble the ball came off a combination Jack Cork, Kieran Trippier and finally the luckless Burnley keeper Tom Heaton before bobbling apologetically into the net.
Burnley???s winless streak was extended to four games and they remain in the relegation zone.
Aston Villa slumped to their sixth straight league defeat ??? and 11th game without a win ??? after going down 1-0 at Newcastle.
Papiss Cisse scored the only goal on 37 minutes, superbly controlling Daryl Janmaat???s cross with his left foot and firing home with his right past Brad Guzan to continue new Villa boss Tim Sherwood???s difficult start.
Peter Crouch scored a record-equalling 46th headed Premier League goal ??? and the only goal of the game – as Stoke beat Hull City 1-0.
Crouch, who had only just come off the bench, headed home from Charlie Adam???s cross on 71 minutes to seal the points for Mark Hughes??? men and equal Alan Shearer???s Premier League headed goals record.
In the early kick-off, Crystal Palace beat West Ham 3-1 at Upton Park, Glenn Murray scoring two goals and then being sent off.
All three of Palace???s goals came from set-pieces, Murray nodding in the first with the help of a deflection off Aaron Cresswell on 43, and Scott Dann then powered in the second with a header from a corner on 51.
Murray helped himself to his second on 63 from a Jason Puncheon free-kick, but was then sent off six minutes later for his second yellow card. Enner Valencia???s goal was the Hammer???s only consolation.