The Bosnian, a £27million signing from Wolfsburg in January, scored the winner in the 75th minute, three minutes after stepping off the bench.
He was embraced by his team-mates after breaking his duck in the top flight in this his 10th appearance. But for Blackburn the prospect of relegation is still a huge threat.
After beating Manchester United and securing a place in the FA Cup final it was no surprise City started brightly.
However, they failed to make their possession pay in the first half especially and Blackburn began to grow in confidence.
But in all came right for Mancini in the end and they are now four points clear of fifth-placed Tottenham.
City almost took the lead in the third minute with a sweeping move that unlocked the home side. Pablo Zabaleta delivered the ball from the right and Gareth Barry touched it to David Silva.
The Spanish forward connected perfectly only to see his shot hit the post and come back out.
Blackburn again found themselves on the back foot four minutes later when City won a free-kick 25 yards out but Mario Balotelli's effort was gathered cleanly by goalkeeper Paul Robinson.
The visitors kept up the pressure and Zabaleta saw his cross cleared by Phil Jones in the 17th minute.
From the resulting corner Barry's header was cleared off the line by Michel Salgado.
Play switched down the other end and Jason Roberts had a claim for a penalty dismissed by referee Andre Marriner following a challenge by Vincent Kompany.
Then Phil Jones showed some invention to go on a galloping run and link up with Martin Olsson before being crowded out.
City responded and Balotelli carved out an opening for himself in the 39th minute only to see his effort blocked.
The momentum was with Blackburn and Chris Samba saw his towering header go narrowly wide of the post a minute later after being set up by Salgado.
City were being stretched and Roberts was allowed room to deliver the ball into the area but Zabaleta made the clearance.
City started the second half like they did the first and Robinson took no chances and pushed over a close-range header from Yaya Toure following a cross from Silva.
However, Blackburn almost took the lead in the 50th minute following a swift counter attack.
Brett Emerton picked out Roberts and his header appeared to be going wide only for Olsson to get on the end of it and send a shot into the side netting.
But it was City who almost edged in front in the 68th minute when Silva carved out an opening only to find the wrong side of the post with his curling effort.
Adam Johnson was replaced by Dzeko in the 72nd minute and the he responded three minutes later with the decisive goal.
Silva supplied the cross and Phil Jones only succeeded in sending his clearance straight to Dzeko, who smashed it home without hesitation.
Blackburn, however, should have drawn level in the 87th minute but Phil Jones headed over from close range and then Olsson's effort was blocked by Joe Hart in stoppage time.
These are worrying times for the home side who remain one point outside the bottom three with four matches to go.