Arouna Kone's late winner moved Wigan out of the Premier League's bottom three and left Norwich only four points above the relegation zone.
The Ivorian was played in by Jordi Gomez before launching a fierce low drive that beat the dive of Canaries goalkeeper Lee Camp.
Martinez proud of winning streak
The goal came just moments after Antolin Alcaraz, James McCarthy and Gomez went close for the Latics.
Norwich's best effort fell to Bradley Johnson, whose shot flew inches wide.
That result means the Canaries have only one victory to show for in their last 14 league games and sit on 34 points.
In contrast, Roberto Martinez's Wigan have recorded three league wins from four. The latest sees them move above Aston Villa on goal difference, with Villa playing Liverpool on Sunday.
The Latics will now go to fellow strugglers QPR next Sunday in good heart and with a strong belief that they will repeat last season's escapology act.
Simon BrothertonMatch of the Day commentator
"Wigan are out of the bottom three. It wasn't a great game but the Latics won't worry about that"
However, for much of the 90 minutes the home team could barely string three passes together, never mind make it three successive victories.
Apart from two Kone chances - one that drifted a foot wide of Camp's post and another which was blocked brilliantly by Sebastien Bassong - they did not look like a team fighting for Premier League survival.
But with 20 minutes remaining, the Latics appeared suddenly to realise what was at stake.
First, Alcaraz tested the Norwich goal with a header that was cleared off the line by Jonny Howson and then McCarthy let fly with an angled effort that whistled past the post.
Norwich did not deserve to lose - Hughton
Gomez, who was one of Wigan's better players, was also denied by some more brilliant Norwich defending when Michael Turner threw himself in front of his shot.
Just as seemed as if Norwich would head back east with a 14th league draw this season, Wigan pierced the last line of defence thanks to the impressive Kone.
The Ivory Coast forward had not been served well by his team-mates all afternoon until Gomez picked him out with a threaded ball. He took the ball in his stride before arrowing a shot inside Camp's near post.
Norwich boss Chris Hughton had brought on Grant Holt seconds earlier, but he was given little time and opportunities to salvage something for his side.
Wigan manager Roberto Martinez:
"I don't think we were stylish as we normally are, but what we showed is an incredible character. Every player found a way to help the team to keep Norwich very quiet.
"To restrict any team in the Premier League to no shots on target requires massive effort. And then it was that little bit of quality at the other end.
"It seemed it couldn't quite fall for us but that's as good a goal as you're going to see in this league. The ball from Jordi Gomez was a fantastic, clinical ball, and the finish of Arouna Kone was just what he deserved for his work ethic."
Norwich boss Chris Hughton:
"When you go away from home sometimes you have to hold your hand up if you've been beaten and beaten well but I don't think anybody seeing the game today would think that.
"We certainly deserved a draw and then it's just going to be about those moments. They had it and we didn't.
"But I thought for an away team we had good periods of the game where we had good control but it's one moment that's beaten us. It's very disappointing."
Full Time The final whistle goes and the game is over.
Franco Di Santo is flagged offside by the assistant referee. Free kick taken by Lee Camp.
Joel Robles restarts play with the free kick.
90:00 +1:41 Substitution
Substitution (Wigan) makes a substitution, with Franco Di Santo coming on for Arouna Kone.
Robert Snodgrass takes a shot. Antolin Alcaraz gets a block in. Unfair challenge on James McArthur by Robert Snodgrass results in a free kick.
Michael Turner gives away a free kick for an unfair challenge on Paul Scharner. Joel Robles restarts play with the free kick.
Free kick awarded for a foul by James McCarthy on Javier Garrido. Lee Camp restarts play with the free kick.
James McArthur concedes a free kick for a foul on Robert Snodgrass. Javier Garrido takes the free kick.
Booking Grant Holt is shown a yellow card for dissent.
Paul Scharner restarts play with the free kick.
Substitution Wes Hoolahan leaves the field to be replaced by Luciano Becchio.
Substitution Alexander Tettey replaces Jonathan Howson.
The referee penalises Bradley Johnson for handball.
Grant Holt gives away a free kick for an unfair challenge on Maynor Figueroa. Direct free kick taken by Antolin Alcaraz.
The referee blows for offside against Grant Holt. Indirect free kick taken by Joel Robles.
Assist by Jordi Gomez.
80:05 Goal scored
Goal! - Arouna Kone - Wigan 1 - 0 Norwich Arouna Kone gets on the score sheet with a goal from the edge of the penalty area to the bottom right corner of the goal. Wigan 1-0 Norwich.
Substitution Grant Holt replaces Kei Kamara.
The ball is swung over by Jean Beausejour, Michael Turner makes a clearance. Inswinging corner taken right-footed by Shaun Maloney from the left by-line, Antolin Alcaraz has a header from inside the six-yard box and clears the crossbar.
Free kick awarded for a foul by Kei Kamara on Maynor Figueroa. Free kick taken by Maynor Figueroa.
Jordi Gomez takes a shot. Blocked by Michael Turner.
Long range effort from James McCarthy misses to the left of the target.
Foul by Kei Kamara on Maynor Figueroa, free kick awarded. Maynor Figueroa restarts play with the free kick.
The ball is crossed by Robert Snodgrass. Kei Kamara is flagged offside by the assistant referee. Joel Robles restarts play with the free kick.
Robert Snodgrass takes a short corner.
The referee blows for offside against Antolin Alcaraz. Indirect free kick taken by Lee Camp.
Jordi Gomez takes a shot. Blocked by Javier Garrido. Outswinging corner taken by Jean Beausejour, Antolin Alcaraz takes a shot. Jonathan Howson makes a clearance.
Maynor Figueroa challenges Wes Hoolahan unfairly and gives away a free kick. Direct free kick taken by Wes Hoolahan.
Substitution James McArthur on for Callum McManaman.
Maynor Figueroa takes a shot from a long way out clearing the crossbar.
Shaun Maloney takes a outswinging corner from the left by-line played to the near post.
Robert Snodgrass crosses the ball, Headed effort from deep inside the area by Kei Kamara misses to the left of the goal.
Shot from just outside the box by Jordi Gomez goes over the bar.
A cross is delivered by Javier Garrido, Kei Kamara takes a shot. Save by Joel Robles.
Centre by Robert Snodgrass, Antolin Alcaraz manages to make a clearance.
The referee gives a free kick against Wes Hoolahan for handball. Antolin Alcaraz takes the direct free kick.
Bradley Johnson has an effort at goal from outside the area missing to the wide right of the target.
A cross is delivered by Robert Snodgrass, Antolin Alcaraz manages to make a clearance.
James McCarthy challenges Bradley Johnson unfairly and gives away a free kick. Wes Hoolahan restarts play with the free kick.
The ball is crossed by Callum McManaman, blocked by Javier Garrido. Corner taken by Jordi Gomez from the right by-line played to the near post, clearance made by Robert Snodgrass. Jordi Gomez produces a cross, Sebastien Bassong makes a clearance. Corner taken short by Shaun Maloney. Shaun Maloney produces a right-footed shot from inside the area that clears the bar.
Jordi Gomez takes the direct free kick.
Booking Elliott Bennett shown a yellow card.
Elliott Bennett gives away a free kick for an unfair challenge on James McCarthy.
The ball is crossed by Russell Martin.
Free kick awarded for a foul by Russell Martin on Jean Beausejour. Jean Beausejour takes the direct free kick.
Jean Beausejour delivers the ball.
Free kick awarded for a foul by Jordi Gomez on Elliott Bennett. Free kick taken by Bradley Johnson.
Shaun Maloney takes a inswinging corner from the left by-line played to the near post, comfortable save by Lee Camp.
Unfair challenge on Michael Turner by Arouna Kone results in a free kick. Lee Camp takes the direct free kick.
The match restarts for the second half.
45:00 +0:58 Half time
Half Time The half-time whistle blows.
Wes Hoolahan handles the ball and concedes a free kick. Joel Robles restarts play with the free kick.
The offside flag is raised against Shaun Maloney. Free kick taken by Lee Camp.
Arouna Kone has an effort at goal from deep inside the area missing to the right of the target.
The ball is sent over by Jean Beausejour, Jonathan Howson gets a block in. Shaun Maloney takes the inswinging corner, Bradley Johnson manages to make a clearance.
Wes Hoolahan takes the chance to get an effort at goal. Blocked by Antolin Alcaraz. Centre by Elliott Bennett.
A cross is delivered by Javier Garrido, Antolin Alcaraz makes a clearance.
Free kick awarded for an unfair challenge on Wes Hoolahan by Shaun Maloney. Javier Garrido restarts play with the free kick.
Arouna Kone takes a shot. Blocked by Sebastien Bassong. Short corner worked by Jordi Gomez.
The offside flag is raised against Wes Hoolahan. Indirect free kick taken by Joel Robles.
Unfair challenge on Wes Hoolahan by Paul Scharner results in a free kick. Direct free kick taken by Bradley Johnson.
Centre by Javier Garrido, save by Joel Robles.
Arouna Kone takes a shot. Save made by Lee Camp. Shaun Maloney is caught offside. Free kick taken by Lee Camp.
A cross is delivered by Jean Beausejour.
Robert Snodgrass concedes a free kick for a foul on Antolin Alcaraz. Jordi Gomez takes the direct free kick.
Kei Kamara takes a shot. Save by Joel Robles.
Foul by Antolin Alcaraz on Wes Hoolahan, free kick awarded. Free kick crossed left-footed by Robert Snodgrass, Paul Scharner makes a clearance.
The ball is crossed by Callum McManaman.
Foul by Maynor Figueroa on Wes Hoolahan, free kick awarded. Wes Hoolahan takes the free kick.
Arouna Kone produces a right-footed shot from just outside the box that goes wide left of the target.
The assistant referee signals for offside against Elliott Bennett. Indirect free kick taken by Joel Robles.
Free kick awarded for a foul by James McCarthy on Wes Hoolahan. Javier Garrido crosses the ball from the free kick left-footed from left wing, Arouna Kone gets a block in.
Shot from outside the penalty box by Elliott Bennett goes wide right of the goal.
Corner taken by Jean Beausejour from the left by-line.
Foul by Elliott Bennett on Antolin Alcaraz, free kick awarded. Free kick taken by Antolin Alcaraz.
Sebastien Bassong has an effort at goal from outside the penalty box which goes wide right of the target.
The ball is crossed by Elliott Bennett, blocked by Maynor Figueroa. Corner taken by Elliott Bennett from the right by-line played to the near post, clearance by Shaun Maloney.
Callum McManaman challenges Javier Garrido unfairly and gives away a free kick. Direct free kick taken by Lee Camp.
Callum McManaman delivers the ball, clearance by Sebastien Bassong.
The ball is crossed by Robert Snodgrass, clearance by Paul Scharner.
Javier Garrido crosses the ball, clearance made by Maynor Figueroa.
Booking The referee books Paul Scharner for unsporting behaviour.
Paul Scharner concedes a free kick for a foul on Robert Snodgrass. Robert Snodgrass restarts play with the free kick. Elliott Bennett takes a shot. Blocked by Arouna Kone. Inswinging corner taken from the right by-line by Robert Snodgrass.
Centre by Elliott Bennett, clearance by Antolin Alcaraz.
The offside flag is raised against Kei Kamara. Joel Robles restarts play with the free kick.
Jean Beausejour produces a cross, Javier Garrido manages to make a clearance. Corner taken left-footed by Jordi Gomez.
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