Boss Manuel Pellegrini named a strong team but City were frustrated by a spirited performance from the visitors in a goalless first half, as City sought a first win in four games.
The contest turned in a frenetic 15-minute period at the start of the second half; Frank Lampard, Edin Dzeko and Jesus Navas netting before Yaya Toure scored from the spot following a foul on Lampard that earned Kamil Zayatte a red card.
Dzeko added the fifth 13 minutes from time and teenager Juan Angel Pozo marked his debut with a late sixth before man-of-the-match Lampard rounded off a 7-0 win.
Willy Caballero replaced Joe Hart in goal to make his first appearance since the Community Shield while Lampard’s emotional point-saving goal against Chelsea on Sunday earned him a second City start.
Wednesday and their sizeable away following travelled across the Pennines full of confidence after just one loss from their opening 10 games this season and they more than matched their hosts in the early stages.
City’s first shot did not arrive until the 16th minute, Bacary Sagna cutting the ball back for James Milner, whose effort lacked the pace to beat Chris Kirkland.
Eliaquim Mangala was making his second successive start and almost scored a stunning first goal for City in the 19th minute.
The big defender met Aleksandar Kolarov’s corner perfectly with a hooked volley but the ball smacked against the near post.
Pellegrini resisted any temptation to make changes at half-time and was rewarded within two minutes of the restart thanks to a deflected Lampard effort.
City did not have to wait long to make it two, Dzeko emphatically converting Navas’ pass for his 10th goal in 11 League Cup games.
And just over a minute later Navas did it all himself, leading Joe Mattock a merry dance on the edge of the area before smashing his shot past Kirkland.
The bad news kept coming for Wednesday as Zayatte was caught out by Milner’s neat ball and tripped Lampard in the penalty area.
As the last man, the defender was shown a straight red card, and Toure found the bottom corner with the spot-kick.
Wednesday almost found a consolation but Caballero blocked Stevie May’s fierce shot and substitute Atdhe Nuhiu could not convert the rebound.
The misery was not over for the visitors, Dzeko adding another to his cup collection in the 77th minute with a towering header from Kolarov’s perfect cross.
In the 88th minute Navas broke away down the right and pulled the ball back for 18-year-old striker Pozo, who slotted the ball calmly through a defender’s legs and into an empty net for City’s sixth goal.
Lampard added the coup de grace by sliding in the seventh with almost the last kick of the game.
Caballero, Sagna, Kolarov Mangala, Demichelis, Fernandinho (Boyata 70), Lampard, Toure (Pozo 64), Milner (Sinclair 73), Navas, Dzeko.
Kirkland, Zayatte, Buxton, Mattock, Lees, Maghoma, Maguire, May, Palmer (Helan 70), Coke (Dielna 61), Madine (Nuhiu 61).
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