City looked well-placed for victory once Martin Petrov had taken just 65 seconds of the second-half to cancel out Charles N'Zogbia's opener in first-half stoppage time.
But the dismissal of Pablo Zabaleta - for a second bookable offence - stopped City in their tracks and they needed Given to make a superb save to deny Hugo Rodallega as they earned a share of the spoils.
There was a paucity of chances for the visitors that did not sit easily with the growing feeling they will be involved in the title shake-up.
In contrast, Wigan, limited as they were, always gave the impression of a side pushing themselves to the limit.
A goalless opening period was drawing to a seemingly inevitable conclusion when Rodallega, set up by the industrious Jason Scotland, went for the far corner with an angled drive.
Given did well to keep it out. But the Republic of Ireland star, named skipper in the absence of Kolo Toure, could only push the ball into N'Zogbia's path and the former Newcastle man beat Wayne Bridge to slide the ball home.
The Blues took just 65 seconds to level after the restart and Carlos Tevez was the creator. After Mohamed Diame had over-run the Argentine's square ball, Petrov was left with a clear sight of goal and he found the bottom corner with a precise shot.
Zabaleta was shown a red for a tackle on Scotland and Wigan were more likely winners.
But Given was equal to Rodellaga's late volley to preserve a point for the visitors.