The Blues went into the Wednesday meeting with a two-win, one-draw lead over reigning champions Manchester City which appeared to be cut to five until Willian struck in the 89th minute at Stamford Bridge.
The goal came in a timely manner for Chelsea, occurring moments after Gareth Barry was sent off for receiving a second bookable offence, and allowed them to retain their lead over City who comfortably won 4-1 at Stoke City.
The Eastlands outfit produced their first triumph over the Potters at the Britannia Stadium in 16 years courtesy of a brace from Sergio Aguero (taking his season tally to 16) as well as goals from James Milner - who netted his second in two matches after a long drought - and Samir Nasri.
The Clarets had produced 10 shots on goal to United's three in the opening 45 minutes but went into the break 2-1 down after defender Chris Smalling headed home either side of Danny Ings' 12th-minute equaliser.
However, the Red Devils were able to maintain their lead before going ahead through Robin van Persie's penalty eight minutes from time to claim their third win their past four league outings.
On the south coast, Southampton dropped back to fourth after being held to a 0-0 draw by ten-man West Ham United at St Mary's Stadium after Hammers goalkeeper Adrian was sent off just after the hour-mark.
West Bromwich Albion grabbed a deserved 2-0 victory over Swansea City at The Hawthorns thanks to second-half strikes from Brown Ideye (2 goals in 2) and Saido Berahino while Alan Pardew's Crystal Palace drew 1-1 with his former club Newcastle United at Selhurst Park with Fraizer Campbell cancelling out Papiss Cisse's 43rd-minute opener.
The Barclays Premier League will return to action on Saturday, February 21 following the fifth round of the FA Cup which takes place on the weekend of February 14 and 15.
2014/15 Barclays Premier League - season scores
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