Dunne had been elbowed by Amr Zaki in an aerial challenge in the second half of a game in which City had just deservedly taken the lead through a Pablo Zabaleta goal in the 53rd minute.
While on the ground it appeared that though Dunne had lashed out against Wigan's Egyptian striker in retaliation for the elbow, but the referee chose to send off only the City captain to the obvious displeasure of the home fans.
Wayne Bridge made his City debut against Wigan in a re-shuffled line-up that saw Robinho return to the side and Nedum Ohuoha start in central defence, with Felipe Caicedo and Gelson Fernandes dropping to the bench and Michael Ball dropping out of the squad.
Micah Richards moved to the right side of defence and Zabaleta pushed up into an unfamiliar central midfield role alongside Vincent Kompany, as they faced a Wigan side unchanged since their midweek game against Manchester United.
Robinho had two golden chances to put City into the lead in the first half. Combining well with fellow Brazilian Elano, Robinho was put clean through, but Maynor Figueroa and Chris Kirkland closed down the space forcing Robinho into a hastily taken shot which went wide of the goal after just 11 minutes.
Elano, who was having a great game in the centre of midfield, was again the provider as Robinho's goalbound chip was kicked off the line by Titus Bramble after 21 minutes.
City looked solid and dangerous in the opening period and Daniel Sturridge could only get underneath Shaun-Wright Phillips' cross from the touchline and the ball sailed over Kirkland's bar from under six yards out a minute after Titus Bramble's clearance.
City were rewarded for their patient build-up with a goal shortly after the break when Zabaleta pounced on a poor Paul Scharner clearance from
Sturridge's cross.
City had precious little time to celebrate as Dunne was sent off minutes later following a controversial aerial challenge with Zaki.
It was all bets off after the red card and City's reduced numbers at least allowed Wigan a couple of openings later on.
But they will regret the most notable of them, when Lee Cattermole hit the bar with six minutes to go and Zaki contrived to miss the open goal with his header from the rebound, while Joe Hart punched a Mario Melchiot chance away in injury time.
Latics boss Steve Bruce was left furious when an injury-time penalty claim was turned down, but City fully deserved the win from their battling performance.