The home side, who started the day just a point above the drop zone, led at the break through Reece James' penalty, after a City defender was adjudged to have handled Sam Morsy's shot.
But Wigan were unable to make the most of several decent chances to double their lead, and City levelled with 10 minutes to go through the prolific Teemu Pukki.
The home side thought they had won it in the eight added minutes, only for Leon Clarke's header to be disallowed for offside - with TV replays showing it possibly should have stood.
Norwich had come flying out of the blocks and top scorer Pukki almost got himself on the end of good work from Onel Hernandez and Todd Cantwell, but Wigan were able to clear.
Wigan too showed up well in the early stages, with Gavin Massey and Morsy both having decent shooting chances that they could not make the most of.
Clarke, on loan from Sheffield United, headed wide from a James cross, before Norwich came within inches of nosing head.
Marco Stiepermann's cross from the left took a touch off a defender on the way through and somehow evaded Pukki at the far post.
But Wigan ended the half on top and deservedly took the lead on the scoreboard.
Lee Evans forced a great save from Tim Krul with a diving header from Antonee Robinson's cross.
But the home side were awarded a controversial penalty when Morsy's shot from 20 yards was adjudged to have struck a City player's arm in the box.
Referee James Linington pointed to the spot, and James beat Krul with a clinical spot-kick.
Norwich had a chance to level within three minutes of the restart, only for Christian Walton to pull off a fine save to deny Hernandez, with Danny Fox clearing up.
James almost made it 2-0 to Wigan with a stinging drive from 25 yards that cleared the bar by a yard.
The home side came closer still when, after a 50-yard run from Kal Naismith, Clarke beat the last man and tried to poke the ball over Krul, who managed to divert it inches past the far post.
James sent other free-kick inches over the top before Norwich made a triple switch with 15 minutes to go, to try to find a way back in.
Morsy almost doubled Wigan's lead only to see his effort fly over off a Norwich shin before the visitors found their equaliser 10 minutes to go.
Kenny McLean did the groundwork in feeding Pukki, who outpaced the Wigan cover before sliding the ball under Walton.
There was still time for Wigan to almost pinch it, but Clarke's header, from James' free-kick, was chalked off for offside.