It was the first Premier League goal in 10 attempts for the Bosnia striker since joining Man City in a 27 million pound ($42 million) transfer from Wolfsburg in January.
Teammate David Silva's shot was only partially blocked by Blackburn defender Phil Jones in the 75th minute, and Dzeko slammed the ball into the net with his less favored right foot only three minutes after coming on as a substitute at Ewood Park.
"Sometimes it's difficult. I'm not the first who didn't make the best start, but I'm happy because I scored today and helped the team," Dzeko said. "Now we have to look at the future. Today was very good — it is a new beginning for me and for City."
City striker Mario Balotelli was standing in front of goalkeeper Paul Robinson when Dzeko scored, and Blackburn manager Steve Kean was unhappy the goal was allowed to stand.
"Balotelli was right in front of Paul Robinson, so I'm saying that was offside," Kean said.
With five matches remaining, fourth-place City is four points clear of fifth-place Tottenham. The two teams are scheduled to meet May 10 at City's Eastland stadium.
Blackburn hasn't won in the league for 10 matches and remains only one point above the relegation zone in 16th place.
Blackburn had claims for a first-half penalty dismissed by referee Andre Marriner when Jason Roberts was challenged by Vincent Kompany in another decision criticized by Kean.
"There was contact, Jason was saying he wanted to go through and finish," Kean said. "We also thought we had a late shout with Niko Kalinic.
"We're bitterly disappointed, we gave it a right go. We're gutted we didn't get anything tonight but if we play like that, we've got a great chance (of staying up)."