However, City showed great bouncebackability to get themselves back in the game five minutes later courtesy of a penalty. Damien Delaney's header was blocked by the hand of Lee Bullen, and Michael Keane stepped up to bury the spot-kick for his fifth goal in all competitions this season.
In the 22nd minute, City did what the home side had done previously, breaking from a corner to take the lead. Ryan France brought the ball out and played it to Delroy Facey in the left channel. Instead of shooting, he unselfishly laid the ball off to Stuart Elliott who was in a better position. Elliott skewed the ball to the back post where Nick Barmby was in an even better position, and the Hull-born ex-England international side-footed the ball into the empty net.
Barmby - who had previously only scored a total of two goals since his summer move to the club - got his second of the night just before half time in spectacular fashion. France glanced a header onto him inside the box, and as the ball dropped over his shoulder he turned and volleyed on the drop to make it 3-1.
Keane did brilliantly to play in Elliott for the chance of a fourth before the break, but Patrick Collins made a last gasp block.
Elliott was also unlucky after the break when his point-blank header from a corner was somehow saved by Owls 'keeper David Lucas.
City were succeeding in killing the game off in the second half, with a number of players wounded in the battle, and nearly scored again 15 minutes from time. Barmby stole the ball on the right wing, and his cross was just too far in front of Danny Allsopp - on as a substitute - whose diving header went wide.
But Wednesday were allowed back into the game in the 81st minute as a defensive mistake gave them a lifeline. Damien Delaney and Leon Cort both went to head the same ball from a long throw-in, and it got to Jon-Paul McGovern at the back post to smash it past Myhill.
But the comeback lasted just two minutes when Allsopp made the win safe for the Tigers. He chased onto Ian Ashbee's long ball and did well to beat the defender to it before hitting a low left-foot shot past Lucas to score his first goal in over 3 months.
A crowd of 28,701 made for a great atmosphere at Hillsborough in a top League One fixture which went City's way on this occassion, 4-2.
City line-up (4-4-2): Myhill; Joseph, Cort, Delaney, Dawson; France, Ashbee, Keane (Lewis 87), Elliott; Barmby (Wilbraham 76), Facey (Allsopp 66).
Un-used subs: Duke, Green.