Mikel Arteta's penalty secured a third consecutive Premier League victory for Arsenal for the first time since March.
Arouna Kone wasted Wigan's best chance when he broke clear in the first half and failed to hit the target.
Arteta scored from the spot just before the hour after Jean Beausejour was penalised for a challenge on Theo Walcott, who again played as a striker.
Wigan have lost six of their last eight games and are in the bottom three at Christmas for the third straight year.
Gunners boss Arsene Wenger joked about coming through a "super crisis" after the 5-2 win at Reading on Monday.
And the Frenchman will take a large measure of satisfaction with the way his team, who were unspectacular but efficient, dealt with a difficult afternoon at the DW Stadium.
With festive matches against Newcastle and Southampton to come, Wenger will be confident his team can enter the new year with a tight grip on a top-four spot.
Although he earned the penalty, Walcott, whose future remains uncertain, was deprived of service for much of the game and the closest he came to scoring was a second-half free-kick.
But his contribution was enough to provide yet more frustration for Wigan.
Wigan manager Roberto Martinez has been hampered by defensive injuries in recent weeks and the loss of a fourth centre-back in Antonio Lopez, who is out for 10 weeks with a hamstring problem, forced him to use a back four against the Gunners rather than three central defenders.
Martinez will be desperate for Gary Caldwell, Ivan Ramis and Antolin Alcaraz to return to action over the festive period.
Arsenal began well and after Arteta was allowed to carry the ball from halfway, he fed Alex Oxlade-Chamberlain, whose drive was pushed past the post by Wigan goalkeeper Ali Al Habsi.
For all of their selection issues, Wigan played with purpose and Kone should have done better when he beat Jack Wilshere and Thomas Vermaelen before hitting a tame shot straight at Wojciech Szczesny.
The Ivory Coast striker threatened again when he was played through by Franco Di Santo and tore away from Per Mertesacker, but his shot squirmed wide.
Wigan full-backs Ronnie Stam and Beausejour were still getting forward at every opportunity, yet Arsenal began to exploit the space behind Beausejour after the interval, with Walcott denied from close-range by Al Habsi when set up by Alex Oxlade-Chamberlain.
It was a policy that paid off when Walcott dropped wide and swapped passes with Santi Cazorla before going down under Beausejour's challenge.
Arteta waited for Al Habsi to dive as he stroked in his third successful penalty of the season.
Wigan responded with Kone cutting in from the left and forcing a save from Szczesny, while Maynor Figueroa had a drive held by the goalkeeper.
David Jones thumped a shot narrowly wide from just outside the area and the hosts had a penalty appeal for a handball against Kieran Gibbs turned down as Arsenal survived a nervous finale.
Wigan boss Roberto Martinez: "That first goal was going to be crucial. The penalty was very soft. Theo was very clever.
"At the other end, it was a clear penalty [for a handball against Kieran Gibbs] because the hands were not in a natural position.
"We are going through a spell where the calls are not going for us, but I am proud of the players. Once all the players are back we will get the rewards."
Arsenal manager Arsene Wenger: "It was hard-fought. Wigan are a good side. We were not as good, sharp and fluent as Monday [when beating Reading].
"It was a tough game and Wigan can surprise a lot of teams. Once we were 1-0 up it was all Wigan but we were well organised. It looked like from outside [that it was a penalty for us]."
Asked if Theo can play up front, he added: "I am convinced he can do that. Today he didn't get that much service but he worked hard and got us the penalty."