Arouna Kone's last-minute goal gave Wigan a vital victory in a game marred by a horror tackle by Callum McManaman on Newcastle defender Massadio Haidara.
Jean Beausejour put the Latics in front when a McManaman cross was not cleared.
McManaman was not punished for a high lunge on Haidara and Magpies assistant John Carver was sent off after trying to confront the forward at half-time.
Davide Santon levelled but Kone won it from a corner which Wigan defender Maynor Figueroa appeared to handle.
The win leaves Wigan three points adrift of safety, with a game in hand on fourth-bottom Aston Villa.
But Newcastle will feel aggrieved, firstly by how McManaman escaped a card for his dangerous challenge and also over Figueroa's handball to flick on the cross that led to Kone's scrambled winner.
Referee Mark Halsey did not even award a free-kick for McManaman's tackle on Haidara, who had been on the pitch for only a matter of minutes after replacing the injured Mathieu Debuchy.
The 20-year-old was eventually stretchered off after lengthy treatment.
Although McManaman did clip the ball, it was his follow through into Haidara's knee that did the damage. Newcastle's coaching staff reacted angrily and, along with Wigan first-team coach Graham Barrow, Carver saw red at half-time after scuffling as the teams headed for the tunnel.
Wigan had dominated the first half, with Newcastle's only meaningful early effort seeing Steven Taylor nod Sylvain Marveaux's corner straight at Latics keeper Joel Robles.
The Latics were well organised at the back and looking to break quickly down the flanks and it was from a cross that they took the lead on 18 minutes.
McManaman beat Haidara and lifted over a delivery that Santon could not clear, allowing Beausejour to pounce and drill home a low shot.
More Wigan chances followed, with Shaun Maloney seeing his curling shot saved and only a last-ditch challenge from Jonas Gutierrez denying James McCarthy after the midfielder burst clear.
And Newcastle remained on the backfoot immediately after the break, with only a smart block by Mapou Yanga-Mbiwa denying McManaman.
McManaman was taken off before the hour mark, bringing boos from the travelling Newcastle fans.
But it was a Magpies switch that appeared to have changed the game, with striker Shola Ameobi replacing midfielder Yoan Gouffran as Alan Pardew moved to a three-man defence that allowed Santon to venture further forward down the right.
The Italy defender did precisely that to level with 18 minutes remaining, latching on to Papiss Cisse's clever pass inside the Latics box after Wigan lost possession and burying a low shot into the bottom corner.
Cisse, who has scored two late winners in the past week, almost struck again from Ameobi's cross but Robles diverted his shot wide.
Instead it was Kone who settled an eventful match. Figueroa used his hand as he leapt to help on McCarthy's corner at the near post and, after the ball bounced around the Newcastle box and James Perch and Santon failed to deal with the danger, the Ivorian was in the right place to slam home from close range.
Wigan manager Roberto Martinez:
"Three points at this stage of the season is huge. We went through a period where we have to score a second goal otherwise it becomes difficult. But I could not be prouder of the character - especially at this stage of the season.
"Without scoring the second goal when we were leading 1-0, we found a way to win.
"The character was magnificent. They were very strong with good individual players who are a real threat.
"I don't feel we have had any luck whatsoever this season and the way we work I think we deserved that luck.
"We had so many opportunities and we couldn't find the final pass so we made it difficult, but we found a way to win and that pleased me."