Adam Johnson, Samir Nasri and Dzeko all scored as Roberto Mancini’s men netted three goals in four first-half minutes to take a commanding 3-1 lead after Nenad Milijas had put the home side ahead.
A Dorus de Vries own-goal and Dzeko’s second of the night put the visitors further ahead soon after the break, before substitute Jamie O’Hara netted a consolation for Mick McCarthy’s side.
The home side started well and took the lead in the 18th minute when Sam Vokes’s low cut-back found Milijas, who smashed a fine effort into the roof of the net.
But the league leaders drew level after 37 minutes when Johnson, clearly looking to prove a point after being completely left out of the City squad for last weekend’s trip to Old Trafford, thumped home a brilliant left-footed effort from just outside the box.
And just two minutes later City were ahead. Johnson threaded an inch-perfect pass through to Nasri, who drilled an early low shot past De Vries in the Wolves goal.
The visitors then stretched their lead a minute later when Dzeko, fresh from his quick-fire brace at Old Trafford on Sunday, bundled home a third to cap a scintillating spell for City before the break.
City started the second half as brightly as they had finished the first. Nasri’s shot was parried by De Vries and Scapuzzi popped up to apply the finishing touch in the 49th minute – a strike which was later confirmed as a De Vries own-goal.
Dzeko then added his second of the night and City’s fifth when he tapped home Scapuzzi’s low cross following a superb sweeping move from the impressive visitors, who have now scored 11 goals in their last two games.
Wolves boss McCarthy responded by throwing O’Hara into the fray and the move immediately paid dividends as the midfielder pulled one back in the 65th minute when he turned home Stephen Ward’s cut-back.
But the damage had already been done and City held firm to secure their place in Saturday’s quarter-final draw.
“I am very happy because of everything. It was not easy. Wolves at home are a difficult team and after they scored the first goal it was difficult, but after that we started to play well and we scored three goals in 10 minutes. It was good.
“He played well, but I think Adam [Johnnson] can do more. He has everything to be one of the best wingers. I liked his performance this evening but I think he can do better.
“One player should never think that if I do this it is enough. Adam has everything, he is one of the best wingers in England and in Europe and I think he can improve.
“When we started the game we were too deep. After they scored we changed and we pushed them very high, it was different.”
Wolverhampton Wanderers: Dorus de Vries, George Elokobi, Jody Craddock, Stephen Ward, Matt Doherty, Nenad Milijas (Adam Hammill, 65), Stephen Hunt, David Edwards (Karl Henry, 67), AdlÃ¨ne GuÃ©dioura, Kevin Doyle (Jamie O’Hara, 65), Sam Vokes.
Manchester City: Costel Pantilimon, Stefan Savic, Pablo Zabaleta, Kolo TourÃ©, Aleksandar Kolarov, Adam Johnson, Samir Nasri (Denis SuÃ¡rez, 67), Nigel de Jong, Abdul Razak (James Milner, 85), Edin Dzeko, Luca Scapuzzi (Karim Rekik, 73).
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