A routine win despite extremely snowy conditions at the Etihad stadium with the Argentine striker in majestic form.
A Sergio Aguero penalty and Chris Barid own-goal had put City two up at halftime before Edin Dzeko stroked home a third to give Roberto Mancini's side an easy win in freezing conditions.
Stefan Savic came into the City back line in place of injured skipper Vincent Kompany with Aleksandar Kolarov and Adam Johnson also replacing Gael Clichy and James Milner.
Martin Jol re-installed Mark Schwarzer to his lineup and opted for Baird rather than John Arne Riise at left back for the Cottagers, while Clint Dempsey partnered Moussa Dembele in attack.
The home side opened the scoring after 10 minutes, Adam Johnson jinking his way into the box before going over Baird's outstretched leg. Mike Dean pointed to the spot and Aguero dispatched the penalty with ease.
The Cottagers were struggling to get a foothold in the game with City dominating possession but they looked to work a way back into the game as Simon Davies' low shot was saved by Hart.
City constantly looked dangerous on the break with Aguero looking particularly ominous. The Argentine tricked his way into the box and with no Fulham players wanting to make a challenge, cut the ball back to Silva who prodded wide.
Fulham was feeding off scraps although Duff worried Hart with a searching effort that almost crept in at the far post.
But City went straight to the other end and doubled the lead. Kolarov's deep cross from the left fell to Johnson who fired the ball back across goal and with Baird unfortunately positioned, the defender was only able to cannon a deflection past Schwarzer.
The home side had another shout for a penalty moments later as Silva went down under Dickson Etuhu's challenge in the box with the Nigerian not seeming to make contact with the ball, but referee Dean declined the Citizens' pleas.
Mancini's men continued on the offensive for the rest of the first half but were unable to breach the Fulham back line again before halftime.
The home side was also forced into making an early change with Nasri limping off with just eight minutes gone in the second half and replaced by James Milner.
As the snow became stronger the action failed to warm up although Stephen Kelly almost troubled an off-balanced Hart with a toe-poked effort, before the England number one dealt comfortably with Baird's rifled free kick.
City was stunned into action. Aguero turned neatly in the box but saw his shot blocked by Danny Murphy before Aleksandar Kolarov curled a close range free kick over the bar.
Soon after City had its third. Aguero picked the ball up on the left flank and darted into the box, breezing past Senderos and Davies before squaring to the unmarked Dzeko who tapped home from eight yards.
With the game all but won for City, Mancini brought off Aguero to a standing ovation and replaced the Argentine with Nigel de Jong to shore up the midfield for the final 10 minutes.
Fulham continued to chase a late goal. Riise stung Hart's palms but the club was unable to find the net and City kept yet another home clean sheet as the team moves three points clear of Manchester United at the top of the table.