After a frustrating, goalless first half, Manuel Pellegrini’s men took the lead just two minutes after the break as Frank Lampard poked James Milner’s cutback beyond Chris Kirkland for his second goal in as many games.
That advantage was soon doubled as Edin Dzeko swept a first-time effort into Kirkland’s bottom corner with a fine finish from Jesus Navas’ low cross.
Navas then got in on the act himself a minute later, lashing a ferocious strike past Kirkland and into the top corner after twisting and turning away from left-back Joe Mattock as he glided into the area.
City were showing no signs of letting up and Yaya Toure added a fourth from the penalty spot as he calmly sent Kirkland the wrong way after Kamil Zayatte was shown the red card for tripping Lampard.
Dzeko then grabbed his second of the night on 77 minutes with a powerful header, before teenage striker Jose Angel Pozo stepped off the bench to add a sixth and Lampard notched his second to make it seven in stoppage time.
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.
Gary Madine had a great chance to test Caballero in the sixth minute when he was picked out by Jacques Maghoma’s cross but he got his header all wrong.
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 Kirkland.
Eliaquim Mangala was making his second successive start and almost scored a stunning first goal for City in the 19th minute, meeting Aleksandar Kolarov’s corner perfectly with a hooked volley which smacked against the near post.
Wednesday’s defensive organisation was limiting City to brief openings, and Kirkland got down comfortably enough to keep out Dzeko’s header.
The hosts tried to up the pace in the closing stages of the first half but the Owls stood firm and fully deserved to go in level after Kolarov’s free-kick flew just off target.
Pellegrini resisted any temptation to make changes at half-time and was rewarded within two minutes of the restart.
Lampard is showing his goalscoring touch applies just as well in sky blue and he finished off good work from Sagna and Milner by bundling the ball in via a deflection.
It was the moment the game needed to come to life and, after Giles Coke forced Caballero into his first save of the night, Navas broke away down the left and crossed for Lampard, who was denied a second by Kirkland.
From the resulting corner, Dzeko attempted a backheeled shot that almost turned into the perfect assist for Martin Demichelis.
However, 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.
The game won, Pellegrini took off Toure and sent on 18-year-old striker Pozo, billed as ‘Mini Messi’.
Pozo joined the club two years ago from Real Madrid’s academy and has been prolific in City’s youth teams.
Milner had been at the heart of everything good for City but was denied a deserved goal by the post before leaving the field to a standing ovation.
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 Pozo, who slotted the ball calmly through a defender’s legs and into an empty net for City’s sixth goal.
Lampard then added the coup de grace by sliding in the seventh with almost the last kick of the game.