Arsenal looked set for a first defeat at the Emirates Stadium after a stunning 35th-minute strike by Wigan's Dutch midfielder Denny Landzaat.
But Wigan defender Fitz Hall's own goal in the 81st minute and an 84th minute winner from Czech midfielder Tomas Rosicky turned the game -- soon after Wigan were denied a penalty.
Arsenal are fourth on 49 points and back in front of Bolton, who had reached 47 points with an earlier 2-1 win over Fulham.
Manchester United, who beat Charlton Athletic 2-0 on Saturday, are top with 66, six ahead of Chelsea who beat Middlesbrough 3-0.
Liverpool are third on 50 points, with Arsenal holding a game in hand on all three.
Wigan will consider themselves very unlucky after leading through Landzaat's stunning 30-metre shot.
They threatened to score more but were floored at the end when Hall turned a cross into his own net and Rosicky headed his first league goal from Julio Baptista's cross.
MANAGER FUMING
Wigan manager Paul Jewell, whose side are one place above the drop zone, was fuming about the lack of a spot-kick for Mathieu Flamini's challenge on Emile Heskey.
"It was a penalty. He puts his hand on his shoulder. Why would Emile want to go down when he's through on goal? The problems with some officials is they don't understand the game."
As for referee Phil Dowd, Jewell told Sky Sports: "Today he's cost our team the points...I've got to be careful what I say but we've been denied victory by bad decisions."
Arsenal manager Arsene Wenger was satisfied with the win.
"It was deserved because we did fight until the last second and they've shown again fantastic fighting spirit and character ...but Wigan could have won as well."
Asked if his side were fortunate not to concede a penalty, Wenger said "Maybe yes...it looked like he could give it."
Wenger was stoical about a booking that rules keeper Jens Lehmann out of the League Cup final on Feb. 25 with Chelsea.
Having preferred Spaniard Manuel Almunia in the competition, he said: "I would not have played him anyway."
Bolton's Gary Speed put them in front against Fulham with a 23rd-minute penalty and Kevin Nolan pounced on a rebound to make it 2-0 five minutes after the re-start at the Reebok. Defender Zat Knight pulled one back for the visitors in the 66th minute.
Bolton manager Sam Allardyce told Sky Sports: "We got two goals in front, deservedly so I think, and played well without having the killer instinct at times. But it was a really good performance and a really good three points."
