An 80th minute goal from Teemu Pukki salvaged a point for City at the DW Stadium after a penalty put Wigan ahead in the first half.
Reece James netted the spot kick for the Lactics in the 45th minute after the referee blew for hand ball in the box.
The Canaries spent the second half searching for a way back into the game, and a brilliant ball from Kenny McLean to Pukki gave City the goal they needed with 10 minutes to go.
Daniel Farke stuck with the same squad who drew 2-2 with Reading midweek, with Emi Buendia still suspended.
An early chance came for City with Onel Hernandez cutting the ball back across goal to Todd Cantwell who tapped it into the path of Teemu Pukki. However, his effort was blocked on the line and cleared away.
Play was pretty even between both sides for the next 10 minutes, with Norwich dominating possession but with no real chances falling for either team.
The first chance of the half for Wigan came 20 minutes in with a good run from Gavin Massey down the right. The Lactics player made it past a sliding tackle from Christoph Zimmermann and put the ball across the box from a tight angle under pressure from Ben Godfrey, but there were no Wigan players waiting to see it home.
Moments later captain Samy Morsy went for goal from distance, but his strike went wide of City’s near post.
Wigan continued to put pressure on City’s defence and were awarded a free-kick on the left of the Norwich goal after Morsy was fouled by Cantwell. Reece James whipped the ball into the box where Leon Clarke got his head to it, but he nodded it just wide.
The Canaries continued to be patient working the ball forwards and with 35 minutes gone Marco Stiepermann played a great pass across goal which looked destined for Pukki to power home, but the Finn couldn’t get a touch on it.
At the other end, Tim Krul was forced into action as Lee Evans headed powerfully at goal, but the Norwich stopper did well to dive and smother the ball. Another chance came for the hosts with a strike from Kal Naismith, which was deflected wide for a corner.
Just ahead of the break, Wigan were awarded a penalty as a Morsy strike was blocked by a City arm. James took the spot kick and found the bottom left corner just past Krul’s reach to give them the lead.
Norwich came out looking for an early equaliser working the ball through to Hernandez who shot low. Pukki looked to pounce on the rebound but the Wigan defence quickly closed him down.
At the other end, James hit a strong effort from distance which flew just over the crossbar and above Krul’s reach.
Just ahead of the 60-minute mark two more chances came for City, with Christian Walton forced to parry away Pukki’s low short for a corner. Tom Trybull then got on the end of a McLean cross, but he headed over.
Wigan made a good break with Leon Clarke racing down the pitch and past the last City defender. Krul made the run out to meet him and got a crucial touch on the ball as Clarke looked to chip it over him, pushing it round the post and out for a corner.
Wigan were awarded a free-kick just outside the box after Zimmermann made a late challenge on Massey. James took the set piece, but his strike sailed inches over City’s bar.
The hosts made a double substitution at 72 minutes with Josh Windass on for Gavin Massey and Nick Powell on for Naismith.
Farke then made a triple change, with Mario Vrancic replacing Trybull, Moritz Leitner on for Jamal Lewis and Jordan Rhodes on for Cantwell.
Minutes later and City went level. McLean fed Pukki who slotted it underneath Walton to bring the Canaries back into the game.
Norwich ranked up the pressure and won three successive corners with Leitner curling each into the box, but the Wigan defence dealt with each attack.
City kept putting the ball in the box and Rhodes managed to get his head to the ball to bring it down for Vrancic to strike, but his shot was blocked and again Wigan cleared it away.
Wigan thought they had scored the winner with Clarke finding the back of the net 94 minutes in, but he was flagged offside.