The Bosnian striker handed his side a 1-0 victory against Blackburn at Ewood Park when he found the target in the 75th minute, three minutes after stepping off the bench.
Dzeko, a ?27million signing from Wolfsburg in January, smashed the ball home at the back post following Phil Jones' misplaced clearance to keep his side in pole position to win the race to fourth place.
He said: "Now we have to look at the future - it is a new beginning for me and for City. I'm very happy that this goal helped my team to win the game. Sometimes it's difficult, I'm not the first who didn't make the best start."
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.
Dzeko added on Sky Sports 1: "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."
Source: PA
Source: PA