Roberto Mancini's side took an early lead through Sergio Aguero's penalty and Chris Baird's own goal increased their advantage before Edin Dzeko sealed the points in blizzard conditions in the second half.
Defending champions United now need to win their tricky trip to Chelsea on Sunday to move back level on points with City at the top.
City, searching for a 12th home victory in as many games this season, had the game under control inside the opening half hour.
Argentine forward Aguero capped an opening 10 minutes of unrelenting City pressure by starting the move that led to the opening penalty -- then converting the resulting spot kick himself.
Aguero's dynamic run past Philippe Senderos ended with a pass to Adam Johnson, who was clearly tripped by Baird as he worked his way into the area.
It was no surprise that City took the early lead and Johnson might have had a second penalty when Baird tripped him on the touchline although this time referee Mike Dean took pity on the Northern Ireland international.
Joe Hart was finally called into action after 24 minutes when he dived smartly to smother a sharp 18-yard shot from Simon Davies and Damien Duff cut in from the right and curled a shot wide just to remind City that a second goal might be required.
But it was Schwarzer who was soon back under pressure as Silva?s low shot flew across the face of goal and Johnson unleashed a wicked 20-yard strike which missed the right-hand post by inches.
A difficult task for Fulham, the last team to earn a league point at City's home ground almost a year ago, was rendered seemingly impossible just before the half-hour when Baird deflected Johnson's cross-shot into his own net.
After Baird's own goal, Aguero's snap shot was parried by the increasingly over-worked Mark Schwarzer and Dzeko was clean through again only to be blocked by Brede Hangeland as City looked to improve upon their pre-match six-goal advantage in the goal difference column over United.
As the snowy conditions worsened in the second half, Fulham finally showed a flicker of life as Clint Dempsey's shot was charged down by Joleon Lescott with the visitors appealing in vain for handball before Danny Murphy produced a shot from outside the area which Hart caught comfortably.
The heavy snow forced delays for the pitch markings to be cleared and the conditions briefly seemed to unsettle City.
Stephen Kelly's darting run and shot tested Hart, who momentarily saw the ball slip from his gloves in all the snow and ice and Baird's 20-yard free-kick beat the City wall and was smothered at the second attempt by the keeper in similar circumstances.
Aguero and City pushed for the comfort of a third goal and Murphy cleared an Aguero effort that was bound for the back of the net.
Dzeko finally settled lingering City nerves after 72 minutes with a goal which owed much to the creativity of Aguero, who sped past Senderos down the left and into the Fulham area before squaring for Dzeko to slot home.
The visitors might have pulled back a consolation after 77 minutes when a Bryan Ruiz corner struck Dzeko and hit the City post, while Hart showed his current dominant form with a late save from Duff.