Tevez had not played for City since refusing to warm up during a Champions League match against Bayern Munich last September but he came on as a 66th-minute substitute to a mixture of cheers and boos from the crowd.
The Argentine striker laid on the winner for Nasri with a brilliant reverse pass in the 85th as City kept up the pressure on Manchester United at the top of the Premier League standings.
"When he plays he knows where to put the ball," City manager Roberto Mancini said. "Carlos did an important pass for Samir, all the fans are happy for this."
Despite the instant impact, Mancini warned the supporters that Tevez needed more time to regain full fitness as the Premier League enters its defining stages.
"Carlos is an important player, but he probably needs two or three weeks to be in good form for the future," the City manager said. "It's not easy for him, but it's important that now he's here."
Tevez came on with City losing 1-0 after Chelsea defender Gary Cahill had scored with a deflected effort in the 60th minute.
Sergio Aguero leveled from the spot in the 78th after Michael Essien handled Pablo Zabaleta's shot before Tevez and Nasri combined for a crucial winner.
"He (Tevez) has showed great spirit and today showed he can be really important until the end of the season," Nasri said. "It's good that it was him that gave the assist."
The result gave City a Premier League record 20th straight home win and cut Manchester United's lead to one point with nine matches left to play.
"We are disappointed because we think we did well (enough) to get something out of this game," said Chelsea manager Roberto Di Matteo as his team suffered a blow in its attempts to reach a Champions League position. "We knew it was going to be a tough game, it's proven very difficult for every team that has come here."
City defender Pablo Zabaleta created the first chance in the fifth minute when he beat Ashley Cole to a bouncing ball in the box and squared for David Silva to screw a shot over the bar.
Fernando Torres, preferred to Didier Drogba up front for Chelsea, looked lively in the opening stages and his strong run at the City defense created a chance that Juan Mata sliced over from just inside the box.
Almost immediately, Nasri almost gave City the lead when he controlled a long ball with his chest and lifted a lob over Petr Cech that hit the bar.
Frank Lampard's wayward pass gave Balotelli the chance to bear down on Cech in the 29th, but the Chelsea goalkeeper made a diving save to tip the shot wide.
The misfiring Balotelli was withdrawn at halftime but the pressure continued, with Yaya Toure and David Silva leading a counterattack in the 50th, only for Nasri to shoot well over from the edge of the box.
Soon after, Nasri's looping cross was palmed onto the bar by Cech, with Silva's backheel deflected wide from the follow-up and Aguero volleying off target from the ensuing corner.
Chelsea's goal came completely against the run of play. Ramires forced a corner on the right wing, City failed to clear the cross and Cahill pounced on the loose ball to hit a shot that bobbled off Yaya Toure to leave City 'keeper Joe Hart stranded.
Tevez was tasked with rescuing the situation after replacing Nigel De Jong and his introduction coincided with an improved tempo from City.
Aguero finally leveled from the penalty spot after Zabaleta's shot ricocheted off Michael Essien's arm in the box.
"I thought it was a harsh decision but probably the right one," acknowledged Di Matteo.
Tevez had a crucial part in the winning goal as his deft pass on the turn allowed Nasri to break into the box and lift a shot over Cech to seal the points for City.
"We did a good performance because we conceded their goal and after things were very difficult," Mancini said. "I was pleased with all the players because I think they spent a lot of energy to win this game."