The Italian insisted ahead of the game that his side would overcome an indifferent start and secure the title they won in such incredible circumstances back in May.
Such fighting talk came after a poor run of form that looked as if it would be extended here in west London as Fulham maintained parity heading into the closing stages.
Mancini's side fell behind to a Mladen Petric penalty after 10 minutes but levelled two minutes before break through Sergio Aguero.
The Argentina international tucked home after a superb save by Mark Schwarzer, who was beaten again at the end by Dzeko.
The Bosnia international had been on the pitch for less than two minutes when he capitalised on a poor clearing header by John Arne Riise and lashed home to secure victory.
The hosts were unable to call upon talisman Dimitar Berbatov for the game after he pulled up with an injury in training this week.
Petric played in his place and was one of two changes made by manager Martin Jol, while there were only three survivors from the City team that fell to a 4-2 extra-time defeat at home to Aston Villa in the Capital One Cup.
City made the brighter start to proceedings, retaining possession with ease as they waited for Fulham's defence to open up.
The hosts extinguished that early threat, though, and were handed a chance to break the deadlock by Mark Halsey.
Pablo Zabaleta tripped Riise after the full-back cut in from the left, which the referee adjudged to be just inside the 18-yard box.
The call looked harsh but Petric made no mistake with his spot-kick, sending Joe Hart the wrong way with a well-struck left-footed effort.
The Croatia international wasted a decent chance to double Fulham's advantage five minutes later as he scooped over after fine link-up play with Hugo Rodallega.
The visitors were remaining patient in their build-up play and it would have paid dividends in the 25th minute had Brede Hangeland not swept clear Zabaleta's driven ball across the six-yard box.
Both sides came close from set pieces as the half-hour mark approached as first Riise saw a venomous 35-yard free-kick saved by Hart.
David Silva then whipped in a corner that was nodded to the back post by Javi Garcia, although Aguero's close-range header could only find the side netting.
City were becoming visibly frustrated by their start to the game and Carlos Tevez confronted Riise after the striker had claims for a penalty waved away.
Gael Clichy tested Schwarzer with a hopeful left-foot drive as the reigning champions pressed for a leveller, although they were still struggling to stifle the Whites at the other end.
Vincent Kompany was booked for bringing down Petric on the edge of the 18-yard box and was fortunate Bryan Ruiz fired wide after the resulting free-kick was blocked.
While Fulham were threatening, they were having to defend at their best to keep City out.
Aaron Hughes and Schwarzer combined superbly to somehow stop the visitors' bundled effort on the line, before the latter showed great reactions to thwart Silva and Hughes cleared from the cross that followed.
But for all that defensive work, Fulham could not quite maintain their lead heading into half-time.
Tevez's deflected shot was turned goalwards by Silva, which forced Schwarzer into a fine save that unfortunately for the veteran fell kindly for Aguero to tuck away.
The tempo slowed as the second half began, as Fulham continued in their attempts to contain City.
After Hangeland came close by connecting with a Ruiz corner four minutes in, most of the play was at the other end and Aguero was unfortunate to see a header loop just wide of the far post.
Mario Balotelli came on for Tevez with 25 minutes remaining as the visitors looked for a new attacking outlet, while Alex Kacaniklic replaced Petric for the hosts.
Five minutes after coming on, both introductions were having an impact as first Balotelli curled wide from the edge of the box.
Kacaniklic then darted down the left and, after seeing an appeal for a handball against Zabaleta turned down, saw his blocked cross fall to Ruiz, whose strike would have nestled in the top corner had it not been for a Hart save.
Giorgos Karagounis came on for his Fulham debut with the clock winding down, while Samir Nasri and Dzeko were brought on in a bid to change the course of the game.
Less than two minutes after the latter's introduction the plan worked as Riise's failure to clear a Clichy cross allowed Dzeko to rifle home inside the box and secure three points.
Source: DSG