It had been a thoroughly forgettable affair until the 76th minute when Phil Neville blocked a Jean Beausejour cross and the ball somehow found its way past Tim Howard for a hugely embarrassing own goal.
But the hosts' lead lasted only seven minutes, substitute Victor Anichebe heading in the equaliser to ensure Everton followed up their win over Manchester City on Tuesday with a point on the road.
Toffees boss David Moyes fielded one of his deadline-day signings, Steven Pienaar, who rejoined the club on loan from Tottenham on Tuesday, but striker Nikica Jelavic had to settle for a place on the bench.
Denis Stracqualursi was the man keeping Jelavic out of the team after impressing against City and he had the first decent sight of goal in the 13th minute, but the ball got stuck under his feet and he could only poke it tamely at Ali Al Habsi.
Pienaar was making his first start in the Barclays Premier League this season but was quickly up to speed and causing trouble for the Latics, who were just about holding firm.
Scoring goals has been a major problem for Wigan and Franco Di Santo could not make the most of a golden chance in the 20th minute. A long ball from Maynor Figueroa caught out the Everton defence but the striker placed his shot too close to Tim Howard.
It was a very scrappy game and Jordi Gomez could only curl a free-kick well over from 25 yards after Johnny Heitinga had hauled down Di Santo, while at the other end Wigan just about managed to scramble a Landon Donovan corner clear.
The Latics were failing to capitalise on good positions, with Victor Moses the latest culprit as his control let him down at the crucial moment as he lined up a shot.
Darron Gibson was the Everton hero on Tuesday but he spurned a good chance five minutes before the break, sending his shot way over the bar after Leighton Baines had done well to get to the goalline and pull the ball back.
Everton made a change at half-time, Neville replacing Tim Cahill, but it did little to improve the quality, with both goalkeepers virtual spectators.
Gibson did manage a half-decent effort but it was easily saved by Al Habsi, and on the hour mark Moyes sent on Jelavic for Stracqualursi. The Croatian was prolific at Rangers and his arrival was greeted with a huge roar from the vocal Everton fans.
Roberto Martinez had also seen enough and in the 65th minute the Wigan manager made a double change, Rodallega replacing Gomez and David Jones coming on for Ronnie Stam, while moments later Di Santo hobbled off and Albert Crusat entered the fray.
The hosts wanted a penalty when Jones' shot deflected behind off Pienaar's arm, but referee Anthony Taylor waved their claims away.
Wigan have been short on luck this season but they certainly got a huge slice of it in the 76th minute as Everton gifted them the softest of goals.
There seemed little danger when Neville got a foot to Beausejour's cross and the ball headed straight for Howard but the keeper let it bounce and the spin on the ball took it past him and into the net, to the disbelief of players and fans alike.
Anichebe came on for Tony Hibbert in the 81st minute in Moyes' final throw of the dice, and within two minutes he had levelled matters, leaping above the Wigan defence to guide in a header from Baines' cross after the hosts had not dealt well with a corner.
Wigan pushed for a winner and almost found it from a late corner but they could not force the ball in as it pinged around the Everton box.
The point did at least end a run of five successive defeats for the Latics, who remain five points adrift of safety.