City were good value for their win thanks to fine long-range strikes from Silva (26) and Barry (37), with Dzeko (47) adding a third shortly after half-time.
But Bolton refused to lie down and made Roberto Mancini's side work hard for the victory with Ivan Klasnic (39) and Kevin Davies (63) both getting on the scoresheet.
Carlos Tevez returned to City colours but Mancini's side showed they no longer need to rely on the Argentinian for goals with a fluent display.
The only negative for Mancini was that City allowed Bolton to stay in the game, Klasnic reducing the deficit just after Barry's superb strike and Davies netting the final goal of the game in the 62nd minute.
The hosts, who like City had won 4-0 on the opening day of the season, kept battling away but there was no doubt the visitors fully deserved the three points to take with them on the short journey home down the M61.
Wanderers were certainly eager to stamp their mark on the game early on but as well as being firm in the tackle they were also troubling City with the speed of their attacks.
Chris Eagles tested Joe Hart with a curling free-kick from 25 yards inside four minutes while Zat Knight shot just past the post after a corner rebounded to him.
City's first incisive attack could have brought the first goal with 15 minutes gone as Silva and Aleksandar Kolarov combined to set up James Milner but Jaaskelainen was out smartly and pulled off a good stop.
Sergio Aguero was given his first start after his stunning showing as a substitute on his debut against Swansea, but he was badly off target as he turned Dzeko's cross over the bar from 10 yards out.
With 25 minutes gone, City did take the lead, although only Jaaskelainen will know how Silva's dipping effort from 20 yards evaded his clutches.
City thought they had scored a second five minutes later when Micah Richards crossed for Aguero to tuck away only for referee Mike Jones to penalise the full-back for a nudge on Martin Petrov.
Mancini's side were certainly bossing things now, though, and Aguero missed another very presentable chance, heading wide from a cross by the impressive Dzeko.
Bolton were struggling to cope and they were two down with eight minutes to go in the first half through a goal of real quality from Barry, who gave Jaaskelainen no chance with a drive into the top corner from 25 yards.
However, Bolton grabbed an unlikely foothold in the game less then two minutes later when a cross from former City winger Petrov was tucked away neatly by Klasnic.
What Bolton needed was a good start to the second half but they got exactly the opposite as Dzeko seized on a flick from Milner before holding off Knight and drilling a shot past Jaaskelainen less than two minutes after the resumption.
It was no less than the Bosnian deserved for his impressive all-round display and City continued to pour forward, with the adventurous Kolarov seeing a shot deflected wide.
However, just when it was beginning to look like a case of how many City would score, Bolton found the net again courtesy of a trademark Davies header from Petrov's free-kick in the 62nd minute.
The one player who was not really impressing for City was Aguero and with 22 minutes to go he was replaced by Tevez, who received a rapturous reception from the visiting fans despite his wish to leave the club.
City threatened again as Silva, who had been at the heart of all their best play, saw a close-range shot brilliantly blocked by Knight while substitute Adam Johnson jinked his way into the Bolton box but pulled his shot just wide of the far post.
Tevez had been very quiet since coming on and it took until injury time for a flash of his talents as he ran purposefully into the box but the eventual shot was weak.