Mancini revealed he had spoken to the ?27million Bosnian to revive his confidence before the trip to Ewood Park and Dzeko repaid his manager two minutes after replacing Adam Johnson.
BLACKBURN 0 MAN CITY 1: READ IAN LADYMAN'S MATCH REPORT HERE Hitting the target: Edin Dzeko (right) beats Blackburn keeper Paul Robinson to seal the points for Manchester City
'Edin is a fantastic striker but he has had some problems because he has not been playing, so he has not scored,' said the manager.
'This was an important goal and he deserved it. I enjoy this moment for him because he has scored a very important goal.'
Making his point: Dzeko has struggled for goals since his ?27million move from Wolfsburg
Dzeko's name was sung continually by City's supporters and he admitted a weight had been lifted.
'Ithink it is a new beginning for me,' he said. 'I have confidence in myself but sometimes it is difficult. I am not the first one that didn'tmake the best of a move. I know in future there will be much better games for me.'
Dzeko's drought has been focused on in parallel with that of Chelsea's ?50million man Fernando Torres, who opened his account against West Ham on Saturday.
A weight is lifted: Roberto Mancini celebrates as his side moved into pole position for a top-four finish
Dzeko added: 'It's football, Torres scored a lot of goals at Liverpool and changed club. I'm happy for him too because I know what the pressure is.'
The substituted Johnson seemed upset at the decision to take him off, and Mancini may have to reassure the youngster.
Stroppy: Adam Johnson is less than happy at being subbed
Mario Balotelli was booked for the 11th time - to go with two red cards - since he arrived from Italy but repeated the wink which so upset Rio Ferdinand in the ill-tempered FA Cup semi-final at Wembley.
Blackburn boss Steve Kean felt Dzeko's goal should have been ruled out for offside as Balotelli stood in front of goalkeeper Paul Robinson.
'We should also have had a penalty, he said. 'We feel hard done by.
'I don't like to moan about referees but we feel their goal was offside with Balotelli standing in front of Paul Robinson.
'We felt we had a good shout for a penalty a bump on Niko (Kalinic) but he probably made it hard for the referee by staying on his feet.
'Full credit to the lads, none of them have anything left. If we continue to approach the games like that we will put points on the table.'
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Explore more:People: Edin Dzeko, Paul Robinson, Rio Ferdinand, Roberto Mancini, Adam Johnson, Mario Balotelli, Fernando Torres Places: Manchester, Liverpool, Italy