United took the lead after just three minutes as Robin van Persie smashed a low drive against the post but the ball cannoned off of David Luiz and nestled in the back of the net.
Van Persie claimed the opening goal, but there was no doubt about the second after another speedy counter attack from the Red Devils saw Antonio Valencia pull the ball back for van Persie to fire home the second with his right foot.
Chelsea gradually got back into the game and Juan Mata scored a superb free kick just before half time after Eden Hazard was cynically brought down by Wayne Rooney right on the edge of the United box.
The inevitable equaliser came just after half time after superb work from Mata and Oscar set up Ramires to powerfully head past David De Gea to level up the match.
Branislav Ivanovic was given a straight red card on the hour mark for tripping Ashley Young who was through on goal and the defender could have no arguments with the decision by the referee.
Just two minutes later Chelsea were down to nine men as Fernando Torres was given a second yellow card for diving when he dribbled past Jonny Evans, a decision that will be debated for weeks. The tensions even spilled onto the touchline as Sir Alex Ferguson and Roberto Di Matteo came together after the red cards.
United substitute Javier Hernandez then added to the controversy by flicking home the winner with just 15 minutes to go despite coming back from an offside position. The decisions really did not go the Blues way for the whole 90 minutes and the fans were happy to vent their anger at the Mark Clattenburg.
Chelsea are still top of the Premier League but their gap has been closed to just one point after United’s win in West London.