The Argentine international ran at the Chelsea defence before jagging to his right and blasting through Ashley Cole's legs and past Petr Cech for the only goal of the game in the 59th minute.
City's win ended the Blues' perfect start to the season and got their own campaign back on track after a slow start.
Manchester City: 1 (Carlos Tevez 59') Chelsea: 0 Venue: City of Manchester Stadium, Manchester Crowd: 47,203 Referee: Andre Marriner Yellow cards:MC - Pablo Zabaleta 35', Dedryck Boyata 77' CH - John Obi Mikel 65', Ramires 80', Alex 90'
MC Joe Hart (gk), Vincent Kompany, Kolo Toure, Pablo Zabaleta, Dedryck Boyata (Boateng 89'), Gareth Barry, Nigel de Jong, Yaya Toure, James Milner, David Silva (Johnson 78'), Carlos Tevez (Adebayor 87')
Subs - Shay Given (gk), Joleon Lescott, Patrick Vieira, Emmanuel Adebayor (87'), Adam Johnson (78'), Jo, Jerome Boateng (89')
CH Petr Cech (gk), John Terry, Alex, Ashley Cole, Branislav Ivanovic, John Obi Mikel (Zhirkov 69'), Ramires (McEachran 81'), Michael Essien, Florent Malouda, Didier Drogba (Sturridge 75'), Nicolas Anelka