City’s 17th successive home league win since Fulham drew 1-1 there almost a year ago, came after Sergio Aguero fired them ahead with a 10th minute penalty after a Chris Baird foul on Adam Johnson.
Baird’s misery continued when he put through his own net 20 minutes later and City added a third from Edin Dzeko after 72 minutes to secure all three points.
City now have 57 points from 24 games with second-placed United, who have 54 points, playing at fourth-placed Chelsea on Sunday. Fulham slipped to 14th, seven points clear of the relegation zone.
Tottenham Hotspur, who are third on 49 points face Liverpool at Anfield on Monday, weather permitting.
In earlier action, Arsenal moved up from seventh to fifth with a crushing 7-1 win over relegation-threatened Blackburn Rovers with Robin Van Persie scoring a hat-trick and talisman Thierry Henry also among the scorers.
Bottom-placed Wigan Athletic drew 1-1 at home with Everton, but Wolverhampton Wanderers, who started the day in 19th place, won 2-1 at Queens Park Rangers and climbed to 17th.
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