Two goals from Mikel Arteta took Wigan's losing run to eight - seven of them in the League - in a match that may have cost Everton the services of their leading goalscorer, Andy Johnson, at a key stage of the season.
The £8m signing was carried off just before the hour and taken straight to hospital for X-rays on his left ankle and lower shin. "We are hoping for the best," said his manager, David Moyes. "It's maybe not as bad as it looks."
Everton toughed out a win in Johnson's absence to leave themselves seventh in the Premiership. "It was dogged and determined," said Moyes, hardly needing to add that it was a long way from being pretty.
All the drama came after a first half of intermittent sleet and hailstorms and even more intermittent bursts of controlled football. The only vague approximations to a goalscoring chance came thanks to the muscular persistence of the Wigan striker Emile Heskey in chasing hopeful balls into Everton territory.
Heskey's efforts created a couple of shooting opportunities, but Arteta found the side-netting and Lee McCulloch, the subject of a bid from Rangers which prompted him to put in a transfer request last week, shot tamely at Tim Howard.
Everton, with Johnson on his own up front, were even less threatening than that, with only a weak effort from Tim Cahill on target or anywhere near the target in the first 45 minutes.
At the other end, dealing with the physical challenge posed by Heskey produced a series of free-kicks from roughly the same position as half-time approached. From one, Howard failed to gather and McCulloch hooked the ball wide, but that was as good as it got.
It had to improve and 10 minutes into the second half Everton began to show signs of life with a header from Joseph Yobo that went just wide and a rising shot from a difficult angle by Simon Davies that needed to be finger-tipped over the bar by Chris Kirkland.
It was then that Johnson suffered his worrying injury, colliding with goalkeeper Kirkland as he chased a ball near the byline.
His departure, on a stretcher in obvious pain, should have robbed Everton of what direction they had, but within a minute of his replacement - the 18-year-old Vincent Anichebe - coming on, he had won the penalty that finally broke the stalemate.
Anichebe went down in a clumsy challenge from the former Evertonian David Unsworth in the blind alley region of the penalty area.
"It was a crazy decision to try to win the ball in the area," said Wigan's manager Paul Jewell, who added that he had no qualms with referee, Howard Webb, pointing to the spot. Arteta fired in confidently.
Wigan had a chance to equalise after that but McCulloch shot wide and Josip Skoko hit the angle of the woodwork with what was by far their best effort of the afternoon.
But the Latics' hopes of ending their dismal run disappeared in the first of five minutes added on for Johnson's injury when Phil Neville's excellent cross from the right penetrated deep into the danger area and Arteta was there first to knock the ball in.
In a game that got livelier in its death throes, Howard had to make late saves from Kevin Kilbane and David Cotterill, but by then Wigan's fate was sealed and their slide goes on.
Goals: Everton: Arteta pen (65) 0-1; Arteta (90) 1-1
Wigan Athletic (4-4-2): Kirkland; Boyce, Hall (Taylor, 64), Unsworth, Baines; Valencia (Cotterill, 77), Landzaat, Skoko, Kilbane; Heskey, McCulloch. Substitutes not used: Filan, Granqvist, Johansson.
Everton (4-5-1): Howard; Neville, Yobo, Stubbs, Lescott; Arteta, Osman, Carsley, Cahill (Beattie, 88), Davies; Johnson (Anichebe, 59). Substitutes not used: Wright, Pistone, Van der Meyde.
Referee: H Webb (Yorkshire).
Booked: Everton: Yobo.
Man of the match: Arteta.