However, the Argentina striker seemed ill at ease as Bolton's five-match unbeaten run came to an end.
Tevez 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 ended the game giving manager Roberto Mancini an ear-bashing when he was replaced by James Milner in the final minute.
City should have won by more than one goal with both Mario Balotelli and David Silva seeing shots come back off the woodwork.
Tevez did not have long to wait until making the breakthrough. 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 Silva's shot was blocked by Cahill. TV Replays showed the ball had come off the defender's shoulder and his arm.
Bolton responded and goalkeeper Joe Hart did well three minutes later to turn a free-kick from former City winger Martin Petrov around the post.
City were having the majority of possession but Tevez in an attempt to win the ball off Sam Ricketts picked up a booking that will see him take a short break.
Then Pablo Zabaleta got into a good position in the area and attempted to lob Jussi Jaaskelainen. But he made mess of it, scooping the ball up and it was easily blocked.
City kept up the pressure and Tevez was being afforded too much room in and around the area. The striker got on the end of a cross from Zabaleta but sent his effort over the bar before miskicking in sight of goal.
Bolton carved out a good chance in the 47th minute when Kevin Davies fired a shot narrowly over the bar following a cross from Ricketts.
Zabaleta, however, nearly made it 2-0 in the 55th minute following a sweeping move that cut Bolton open.
It was started by Silva, who was putting in a hard shift. He picked out Yaya Toure and he played the ball on to Zabaleta.
The full-back made good contact but Cahill was well positioned and cleared it to safety.
Bolton were being over-run at this stage and Balotelli was beginning to make an impact after a quiet first half.
He smacked one effort against the outside of the post before seeing another booted clear by Jaaskelainen.
Then Silva was out of luck in the 61st minute with a quick turn and shot that rattled the bar.
Bolton were struggling but Johan Elmander tried his luck with an overhead kick four minutes later that ended in the arms of goalkeeper Hart.
They almost equalised in the 71st minute following an error by Hart, who climbed on the back of Joleon Lescott when Ricketts delivered a free-kick from distance.
The ball finished behind the England goalkeeper but luckily for him Vincent Kompany cleared off the line.
City were then reduced to 10 men in the 79th minute with Kolarov picking up his second booking of the game for a challenge on Ricketts.
Tevez then vented his anger at Mancini as City went on to seal a narrow win.