The Argentine forward's excellent solo run from the halfway line ended with a right-footed strike through Ashley Cole's legs and past keeper Petr Cech as the ball hit the left post on its way into the net in the 59th minute.
Coming into the match with too few fit defenders against a team who had scored 21 goals in five matches was not ideal preparation but City coach Roberto Mancini brought in young Dedryk Boyata at right-back, also adding pace to that flank.
Keeper Joe Hart did not have a save to make as Vincent Kompany and Kolo Toure dealt calmly with rare Chelsea threats but it was in midfield where the battle was won with Nigel de Jong and Gareth Barry pivotal in winning and keeping the ball.
Yaya Toure and James Milner built the momentum forward, while David Silva was lively although still lacking an instinctive connection with Tevez.
Despite his team being the first to tame the league leaders, Mancini still believes the Londoners will retain the title.
"I think Chelsea is the better team in the Barclays Premier League. I think they will probably win the title," he told a news conference.
"It is not possible that they score four or five goals every game, sometimes (it is) like today, but I think they are a better team."
MOTHER'S BIRTHDAY
Chelsea coach Carlo Ancelotti put the defeat down to a bad day at the office, with Didier Drogba barely threatening and Florent Malouda also quiet. Michael Essien provided most of the attempts but his speculative long-range shots went well wide.
"It is not a good place for us," said the Italian. "It was not a good performance by the team. We did well five times, we missed this time."
Tevez lived up to his reputation as a thorn in Chelsea's side after scoring in both of City's wins over Chelsea last season. Despite his individual brilliance, he refused to lap up the glory.
Instead he diverted attention to a birthday greeting to his mother which he revealed when he pulled up his shirt in celebration and when he got a standing ovation he responded by applauding the crowd.
"Carlos is a fantastic striker, not only because he scores goals but because he fights every time against tall players on every ball," said Mancini, criticised by some fans and media after a less than assured start to the season despite heavy spending in the transfer market.
While City are far from the finished article with their expensively assembled team still working out how to gel, they proved to their critics that they can compete with the top four.
"We must continue to work every day," said Mancini, determined not to get carried away. "We must not think that because we won this game everything is OK."
