City handed home debuts to Adam Johnson and Patrick Vieira and faced a Bolton side crucially without defender Gary Cahill, who was missing with a blood clot in his left arm.
Both City players were to become crucial in a game of vital importance to both sides.
Mindful of their leaky defence in recent games, City used the height and experience of the solid defensive midfield trio of Nigel de Jong, flanked by Vieira and Gareth Barry to counter the expected physical Bolton approach.
The first half plaudits, however, went to home debutant Johnson whose enthusiasm and pace proved hard to counter down City's right flank.
It was Johnson whose attacking ethic prised open the Bolton defence on several occasions in the first half, eventually earning a penalty for City after 31 minutes.
Tevez gave City the lead from the spot when livewire winger left Arsenal prodigy Jack Wilshire trailing in his wake and was tripped by Paul Robinson as he tried to go round him at the byline and into the box.
The Argentine striker powered his penalty at Jussi Jaaskelainen, whose outstretched left hand took the sting out of the strike but the Finn could only watch in despair as the ball spun off his hand and rolled into the back of the net.
The second half saw Tevez rattle the Bolton bar after 52 minutes and Johnson's far post cross-shot had home fans out of their seats, but it took until the 73rd minute for City to make the game safe with the move of the match.
Adebayor was relishing linking up with his old Arsenal team-mate and there was a genuine flash of brilliance when Vieira turned creator from deep in midfield.
Vieira launched a 35-yard direct pass onto the chest of the Togolese striker, who turned and volleyed past a helpless Jaaskelainen.
City's two-goal cushion forced Bolton into a more aggressive stance in a bid to get themselves back into the game but Roberto Mancini's side were capable of holding onto the lead comfortably.