City, whose billionaire owner Sheikh Mansour has spent hundreds of millions transforming the club into title challengers, lead the early standings on goal difference from Wolverhampton Wanderers who also have six points from two games after their 2-0 win over Fulham.
Champions Manchester United will join the leaders if they beat Tottenham Hotspur at Old Trafford on Monday when Spurs finally kick off their campaign after last week's season-opener against Everton was called off following the London riots.
City, who beat Swansea City 4-0 on Monday, took their tally to seven goals from two matches with another fine attacking performance sparked by Silva who opened the scoring after 26 minutes with a low shot that Bolton keeper Jussi Jaaskelainen allowed to slip through his grasp.
The Finnish keeper had no chance with the next long-range effort 12 minutes later when Gareth Barry thundered the ball home, but Bolton, who started the match in good spirits after their opening 4-0 win at Queens Park Rangers, were quickly back in contention.
A fine move ended with Martin Petrov crossing for Ivan Klasnic to sweep a low volley past Joe Hart, but City regained their lead two minutes into the second half when Edin Dzeko maintained his good run of scoring form with a well-taken drive after holding off Zat Knight.
Resilient Bolton came back again when Kevin Davies outjumped Joleon Lescott to head their second after 63 minutes.
But City held firm, finishing the match with substitute Carlos Tevez on the pitch in place of a tiring Sergio Aguero, a sight many City fans did not expect to see again following a summer in which he has made no secret of his desire to leave the club.
City manager Roberto Mancini said he was relieved to leave with three points.
"I can't believe we suffered all the way to the end, but Bolton are a good team and tried to score," the Italian told Sky Sports.
"But we can't concede two goals like we did, we have to pay more attention."
City, who have qualified for the Champions League for the first time and are chasing their first title since 1968, have started well but Mancini knows they still have to improve to wrest the crown from United.
"We need to score 15 more goals than we did last season and concede less if we want to have a good season," he said.
GOOD START
Wolves, who won the last of their three titles in 1959, have no real chance of repeating that but have made their best start to a top-flight campaign since 1979 by following up last week's win at Blackburn Rovers with victory over Fulham.
They went ahead when Kevin Doyle finished clinically after riding two challenges after 42 minutes and they doubled their lead through Matt Jarvis just before half-time.
It was Fulham's first defeat in nine matches since Martin Jol took over at Craven Cottage but the Dutchman was keen to play down his team's involvement in the Europa League.
