While City handed full league debuts to Patrick Vieira and Johnson, Bolton handed a first career Premier League start to Jack Wilshere, the promising 18-year-old midfielder on loan from Arsenal, and he was instrumental in an enterprising first half display from the struggling visitors.
City might have been made to pay for wasting so much early possession when Bolton's 16th minute counter-attack ended with Johan Elmander firing wide from the edge of the area.
In the 37th minute, the City defence reacted slowly and allowed Fabrice Muamba to connect with a powerful 25-yard shot, which took a deflection and forced Shay Given into a magnificent diving stop.
Adebayor wasted a glorious chance to put Bolton away before the break when Sam Ricketts misjudged a cross to leave the City man clean through only for him to screw his shot wide, although yet more uncertainty in the home defence might have seen the scores level at the interval.
Wilshere shot at Given from 15 yards and Gareth Barry?s handball presented Bolton with a free-kick on the edge of the area, which Tamir Cohen powered directly into the wall.
An early second half injury to Kolo Toure forced City into a defensive change, with the 24-million-pound substitute Joleon Lescott brought on.
With Lescott warming up, City almost doubled their lead when Cohen handled 20 yards from his goal and Tevez sent a terrific free- kick sailing against the Bolton bar with Jaaskelainen rooted to his line.
There were reminders that City might yet need a second goal; Cohen's touch played in Elmander whose shot on the turn flew just inches wide.
The cushion of that second goal finally came in the 73rd minute after a brilliantly-weighted pass from Vieira caught Ricketts playing Adebayor on-side.
The City forward controlled the ball brilliantly on his chest with his first touch before producing an unstoppable 15-yard finish.
Bolton's last glimmer of a comeback ended in the 80th minute when South Korean international Chung-Yong Lee found himself through on goal but could only shoot harmlessly at Given.

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