The Blues finished the match with nine men after Branislav Ivanovic and Fernando Torres were both questionable sent off in the second half as Javier Hernandez came off the bench to slot home a late winner for United despite there being a hint of offside.
An early goal for the Red Devils came inside five minutes when Chelsea defender David Luiz was desperately unlucky to see Robin van Persie's shot deflect off the bar and onto him before advancing into the back of the net.
van Persie then put United two goals to the good in the 12th minute when he came up with a first-time finish on his non-preferred right foot to sweep home Antonio Valencia's low drive across the goal-face.
Chelsea picked up their output after falling two behind and were peppering the United goal late in the first half before Juan Mata made it seven goals in his last six outings in all competitions with a sublime free-kick which nestled into the right side of David de Gea's goal.
Chelsea's comeback from two goals down was complete early in the second half when Ramires rose above Tom Cleverley to nod home Oscar's cross from the left after Mata had floated across goal after keeping the ball in pay near the byline.
Referee Mark Clattenburg made a very questionable decision just after the hour-mark when he sent off Ivanovic for felling Ashley Cole as he bore down on goal but the replay showed that the Serbian defender accidentally clipped the heels of the winger.
Chelsea's day got worse with just under 20 minutes remaining when Torres was given his marching orders for a second bookable offence, this one for simulation when he went down easily after a tackle from Jonny Evans. There was minimal contact but Torres made the most of it, however, he too can count himself unlucky to be heading to the dressing room prematurely.
With just over 15 minutes remaining, substitute Chicharito gave United the lead when he diverted home Rafael's fierce drive after Petr Cech somehow kept out van Persie's attempt, with the ball dropping to the upright before the Brazilian was on hand to shoot on sight.
de Gea was on top of his game with a number of vital saves, namely when he unorthodoxly kept out Luiz's brilliant dipping free-kick in the 24th minute with his legs.
In the 42nd minute, it was again de Gea who saved his side when Torres played in Mata following his goal but the Spaniard denied his countryman's left-footed stab, again with his legs.
Ten minutes into the second half, the United keeper came up with a third save with his legs to thwart Hazard's fired effort whilst Valencia had the chance to wrap it up in injury-time but put his effort well wide from an angle as United blew the title race wide open by stalling the run of the league leaders.
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