Rangers took the lead through Jay Bothroyd before being pegged back by a Dzeko strike and clever David Silva goal, but they grabbed an equaliser themselves in the 69th minute thanks to Heidar Helguson.
Back came Roberto Mancini's side though, and Yaya Toure secured the win with a header 16 minutes from time.
Despite beating Warnock’s side, Dzeko had nothing but admiration for QPR, claiming City haven’t had a harder match away from home so far this term.
"It was a really tough match but in the end we can be happy,” the Bosnian told ESPN.
"I think this is the best team we have played against away from home this season and I want to give my compliments to Queens Park Rangers.
"I was really surprised with how well they played, especially in the first half and then later on in the second half with the way they came back after we had gone ahead."
After a fairly tame first half effort from City, Toure claimed the aim at half time was to dig in and continue to work hard, while the Ivorian also spoke about how he is enjoying his current goal-scoring form.
He said: "At half-time the message was to continue to play hard because it is difficult to play away from home and especially with QPR and the way they were playing made the game very tough.
"They put us under pressure in the first half which was difficult but that is a fantastic result for us in the end.
"The team is working well and I'm very happy with what I have done for the team but the most important thing is the team as a whole and if we can continue like that it will be fantastic."