The Argentinian was instrumental in creating Roque Santa Cruz's opener and he added the second himself with a wonderfully taken goal to give his side a two goal advantage at half-time.
Danny Murphy gave Fulham hope from the penalty spot 15 minutes from time but the visitors fully deserved their win.
There is no doubt now that City are favourites to take the final slot available for a place in Europe's premier competition next season - they sit fifth, two points behind Tottenham but with a game in hand.
Tevez served notice of his mood just two minutes into the game after rasping a 30-yard drive that brought an athletic diving save from Fulham goalkeeper Mark Schwarzer.
Just seconds after Zoltan Gera's close-range effort for the hosts was cleared off the line by Kolo Toure, Tevez initiated a counter-attack that ended with the ball in the back of Fulham's next.
Wriggling into space, the Argentinian played the ball into the feet of Craig Bellamy, who ran towards goal and fired a right footed shot.
A deflection off Fulham defender Aaron Hughes sent the ball onto the post, evading goalkeeper Mark Schwarzer as it fell for Santa Cruz to tap home just his third Premier League goal of the season.
In the 36th minute, Tevez doubled the advantage superbly after finishing a flowing passing exchange with Bellamy by cutting inside Manchester United-bound Chris Smalling and turning the ball past Schwarzer with aplomb for his 22nd of the season.
After the break, Santa Cruz forced Schwarzer into a smart save before winger Adam Johnson cut in from the right and saw his fierce striker graze the outside of the post.
Roy Hodgson's side, having created very little of note, were all of a sudden back in the 75th minute when Gareth Barry clearly handled Chris Baird's cross and referee Lee Probert awarded a penalty which Murphy converted.
Fulham substitute Stefano Okaka could have levelled but he could only sweep his shot into the side-netting.
The home crowd roared for another penalty after Vincent Kompany appeared to handle in added time but the appeals were waved away.
The visiting fans sighed with relief but their side's top four challenge continues to gather pace.