Wigan are now nine league games without a win after Everton's Victor Anichebe came off the bench to equalise late on.
A dull game came to life in the last 15 minutes when Phil Neville tried to cut out Jean Beausejour's cross.
His interception bounced towards Tim Howard - but the Everton goalkeeper was deceived by the spin and the ball looped into the net for an own goal.
But bottom side Wigan, without a win since 10 December, were denied victory when Anichebe powerfully headed home.
For Everton, so impressive in beating leaders Manchester City in midweek, it was a disjointed performance, despite a strong showing from Steven Pienaar after his return to the club on loan from Tottenham .
The South African, supporting lone striker Denis Stracqualursi from the flank, made all the running in a dull opening half-hour, on one occasion superbly beating three men in midfield only to find his Argentine team-mate offside.
Franco Di Santo went close for the hosts when he latched on to a long ball from Maynor Figueroa but Howard was swiftly off his line to save at his feet.
But it was Darron Gibson, match-winner against City, who spurned the only clear chance of the first half.
Former Wigan left-back Leighton Baines burst down the left and cut it back perfectly for the former Manchester United man, who thrashed his effort high and wide.
"Tim Howard is usually one of the most reliable goalkeepers in the league but he was beaten like Matt Prior off a spinning wicket in Abu Dhabi. Wigan are still five points away from safety and they have Bolton away next weekend."
Everton boss David Moyes introduced captain Neville for the injured Tim Cahill at the break but, despite more bright play from Pienaar and Landon Donovan, they could not manage a breakthrough.
The biggest cheer of the day came when Everton's new £5.5m striker Nikica Jelavic came on for Stracqualursi, and the Croatian was involved immediately as he cleverly stepped over a Tony Hibbert cross but Wigan cut the ball out before Marouane Fellaini could reach it.
Stalemate was then averted as Neville inadvertently put Wigan ahead.
The impressive Beausejour fizzed in a cross from the left which Neville cut out at the near post, only for Howard to be beaten by the spin.
Everton rallied almost immediately, however, levelling the scores with eight minutes remaining when a corner from Baines was returned to the full-back. His second cross found Anichebe, who scored with a powerful header.
Wigan manager Roberto Martinez remained upbeat despite his club's predicament, five points from safety.
"It was a very good performance and we are obviously desperate to get points," he said.
"In the last two games we have been disappointed with ourselves and got a little cagey but I really enjoyed the performance today.
"We got on the ball, created chances, scored the first goal and we got punished when we had a period of not being able to control the game."
Moyes felt his side had not fully recovered from their exertions against Manchester City.
"Our efforts in midweek told on us today, but after we went goal down we lifted it," said the Scot.
"It was a massive deflection off the pitch for their goal, but we never looked like we were going to concede and it was just whether we were going to do enough to score at the other end.
"I thought Steven Pienaar was the best player on the pitch by a mile - he made us play better football and he has lifted the dressing room. You never know what you are getting back but he was superb."
Live Text Commentary
Full Time The referee blows his whistle to end the game.90:00 +3:09
Unfair challenge on Jean Beausejour by Nikica Jelavic results in a free kick. Free kick taken by Gary Caldwell.90:00 +2:01
Albert Crusat is penalised for a handball. Tim Howard restarts play with the free kick.90:00 +1:06
Corner taken by David Jones.87:24
Leighton Baines fires a strike on goal direct from the free kick.87:24 Booking
Booking Maynor Figueroa shown a yellow card.87:15
Nikica Jelavic fouled by Maynor Figueroa, the ref awards a free kick.85:11
The assistant referee flags for offside against Victor Anichebe. Free kick taken by Ali Al Habsi.82:32
Assist on the goal came from Leighton Baines.82:32 Goal scored
Goal! - Victor Anichebe - Wigan 1 - 1 Everton Victor Anichebe finds the back of the net with a headed goal from close range. Wigan 1-1 Everton.82:29
Inswinging corner taken from the left by-line by Leighton Baines.81:47
Landon Donovan takes the inswinging corner, Nikica Jelavic takes a shot. Gary Caldwell gets a block in. Steven Pienaar challenges Gary Caldwell unfairly and gives away a free kick. Direct free kick taken by Gary Caldwell.80:09
Indirect free kick taken by Ali Al Habsi.80:09 Substitution
Substitution (Everton) makes a substitution, with Victor Anichebe coming on for Tony Hibbert.80:09
The referee blows for offside.75:02
Assist by Jean Beausejour.75:02 Goal scored
Goal! - Phil Neville - Wigan 1 - 0 Everton An own goal is scored by Phil Neville. Wigan 1-0 Everton.74:14
Free kick awarded for a foul by Landon Donovan on Jean Beausejour. Gary Caldwell takes the free kick.72:13
The offside flag is raised against Leighton Baines. Indirect free kick taken by Ali Al Habsi.70:40
Unfair challenge on Leighton Baines by James McArthur results in a free kick. Leighton Baines takes the direct free kick.
David Jones takes a corner.67:55 Substitution
Substitution Franco Di Santo leaves the field to be replaced by Albert Crusat.67:31
Marouane Fellaini is ruled offside. Gary Caldwell takes the free kick.63:29 Substitution
Substitution David Jones comes on in place of Ronnie Stam.63:29 Substitution
Substitution Hugo Rodallega on for Jordi Gomez.61:08
The referee gives a free kick against Nikica Jelavic for handball. Direct free kick taken by Ali Al Habsi.59:11
Indirect free kick taken by Johnny Heitinga.59:11 Substitution
Substitution (Everton) makes a substitution, with Nikica Jelavic coming on for Denis Stracqualursi.59:11
Franco Di Santo is flagged offside by the assistant referee.58:51
Darron Gibson takes a shot. Save made by Ali Al Habsi.55:36
Free kick taken by Leighton Baines.55:36 Booking
Booking The referee cautions James McArthur for unsporting behaviour.55:25
Foul by James McArthur on Steven Pienaar, free kick awarded.53:33
The offside flag is raised against Franco Di Santo. Indirect free kick taken by Johnny Heitinga.52:50
Maynor Figueroa fouled by Marouane Fellaini, the ref awards a free kick. Direct free kick taken by Ali Al Habsi.50:59
Free kick awarded for an unfair challenge on Jean Beausejour by Marouane Fellaini. Jean Beausejour takes the free kick.45:01
The second half begins.45:01 Substitution
Substitution (Everton) makes a substitution, with Phil Neville coming on for Tim Cahill.45:00 +0:58 Half time
Half Time The ref blows to end the first period.44:59
Marouane Fellaini concedes a free kick for a foul on Emmerson Boyce. Ali Al Habsi restarts play with the free kick.44:29
Free kick awarded for a foul by Jean Beausejour on Landon Donovan. Free kick taken by Johnny Heitinga.43:37
Steven Pienaar is penalised for a handball. James McArthur takes the direct free kick.42:37
Tim Cahill fouled by Jordi Gomez, the ref awards a free kick. Tim Howard takes the free kick.39:25
Darron Gibson has an effort at goal from deep inside the area missing to the right of the goal.36:54
Franco Di Santo gives away a free kick for an unfair challenge on Tony Hibbert. Tim Howard takes the free kick.35:39
Franco Di Santo challenges Darron Gibson unfairly and gives away a free kick. Direct free kick taken by Sylvain Distin.33:15
Ronnie Stam challenges Steven Pienaar unfairly and gives away a free kick. Direct free kick taken by Leighton Baines.31:53
Denis Stracqualursi is ruled offside. Gary Caldwell takes the indirect free kick.29:44
Shot from just outside the box by Steven Pienaar misses to the right of the goal.28:59
Corner from left by-line taken by Landon Donovan.27:03
Unfair challenge on Franco Di Santo by Johnny Heitinga results in a free kick. Jordi Gomez has a direct shot on goal from the free kick.25:12
The referee penalises Tim Cahill for handball. Ali Al Habsi takes the direct free kick.24:09
Free kick awarded for a foul by Emmerson Boyce on Denis Stracqualursi. Johnny Heitinga takes the direct free kick.22:09
Free kick awarded for a foul by Jean Beausejour on Denis Stracqualursi. Darron Gibson restarts play with the free kick.21:08
Corner taken by Jordi Gomez, Tim Howard makes a save.19:47
Franco Di Santo takes a shot. Save by Tim Howard.17:05
The assistant referee signals for offside against Denis Stracqualursi. Gary Caldwell restarts play with the free kick.15:32
Landon Donovan challenges Jean Beausejour unfairly and gives away a free kick. Ali Al Habsi takes the direct free kick.12:25
Denis Stracqualursi takes a shot. Save by Ali Al Habsi.11:53
Unfair challenge on Steven Pienaar by Ronnie Stam results in a free kick. Free kick taken by Leighton Baines.11:08
The referee blows for offside against Denis Stracqualursi. Gary Caldwell restarts play with the free kick.9:46
Tim Cahill fouled by Emmerson Boyce, the ref awards a free kick. Johnny Heitinga takes the direct free kick.8:52
Shot from just outside the box by Tim Cahill misses to the right of the goal.6:42
Corner taken by Jean Beausejour, Tim Howard makes a save.4:56
The referee blows for offside. Indirect free kick taken by Ali Al Habsi.0:33
The official flags Franco Di Santo offside. Indirect free kick taken by Sylvain Distin.0:00
The referee gets the game started.
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