Second-half substitute Dzeko, signed for £30 million from VfL Wolfsburg in January, pounced on a loose ball eight yards out after 75 minutes to leave City on 59 points from 33 matches, five points behind third-placed Arsenal with a game in hand.
This season's FA Cup finalists also pulled four points clear of fifth-placed Tottenham Hotspur who, like City, have played 33 games, and the relief on Dzeko's face after notching his first Premier League goal was clear to see after the match.
"I'm not the first one who hasn't made the best of himself," he said, referring to Chelsea's January signing Fernando Torres who scored his first goal for the London club on Saturday.
"I'm happy also for him. I know what the pressure is," Dzeko told Sky Sports.
FRENZIED START
The visitors started at a frenzied pace and could have scored inside three minutes when David Silva cracked a left-footed volley on to the post.
After weathering Blackburn pressure in the second half, City struck when Silva's shot was diverted into Dzeko's path and he finished clinically although television replays suggested fellow striker Mario Balotelli was offside and impeding goalkeeper Paul Robinson.
Keeper Joe Hart produced a smart save from Blackburn's Martin Olsson late on, leaving City manager Roberto Mancini with a big grin after the game.
"I am very happy for Edin. He deserves to score because he is a good player, a good man," said Mancini.
Midfielder Nigel de Jong said Manchester City, who also play Stoke City in next month's FA Cup final at Wembley, were looking to end the season in style.
"We have to aim at the highest possible place in the league. We have to keep focused and maybe we can come third, you never know," said De Jong.
Blackburn are in a relegation battle, one point ahead of 18th-placed Wigan Athletic and only three in front of bottom club West Ham United.
