But the Argentinian striker picked up his fifth booking of the campaign and will miss the match against West Ham on Saturday. So too will Aleksander Kolarov, who is also banned after being dismissed by referee Andre Marriner after picking two yellow cards.
Tevez did not have long to wait until making the breakthrough against the Trotters. Yaya Toure slipped the ball through the middle in the fourth minute and Gary Cahill failed to deal with it. That allowed the club captain to drill a shot into the corner for City's first goal at home since October.
City then made an unsuccessful appeal for a penalty in the 14th minute when David Silva's shot was blocked by Gary Cahill. TV Replays showed the ball had come off the defender's shoulder and his arm. Bolton carved out a good chance in the 47th minute when Kevin Davies fired a shot narrowly over the crossbar.
Zabaleta made good contact with a shot but Cahill cleared and Mario Balotelli smacked one effort against the outside of the post before seeing another booted clear by Jussi Jaaskelainen. Silva was then out of luck with a quick turn and shot that rattled the bar.
Bolton almost equalised in the 71st minute following an error by Joe Hart, who climbed on the back of Joleon Lescott when Sam Ricketts hit a free-kick. The ball finished behind him but Vincent Kompany cleared. City were reduced to 10 men in the 79th minute with Kolarov picking up his second booking.