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.
Hard-fought win pleases Wenger
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
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.
Paying the penalty
Wigan have conceded 14 penalties since August 2011, more than any other Premier League side
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.
Martinez questions Arsenal penalty
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."
Full Time The referee blows for the end of the match.
Jean Beausejour produces a cross, Per Mertesacker makes a clearance. Effort from inside the area by James McArthur misses to the right of the target.
90:00 +1:04 Substitution
Substitution Santi Cazorla goes off and Laurent Koscielny comes on.
Jordi Gomez takes a shot. Per Mertesacker gets a block in.
Shot from 25 yards from Jordi Gomez. Blocked by Per Mertesacker.
Substitution Jordi Gomez replaces Shaun Maloney.
James McArthur has a headed effort at goal from deep inside the area missing to the left of the target.
Mikel Arteta gives away a free kick for an unfair challenge on Maynor Figueroa. James McCarthy takes the direct free kick.
Francis Coquelin fouled by Shaun Maloney, the ref awards a free kick. Wojciech Szczesny takes the free kick.
Mikel Arteta restarts play with the free kick.
Booking Booking for Shaun Maloney.
Shaun Maloney gives away a free kick for an unfair challenge on Francis Coquelin.
Centre by Callum McManaman.
Outswinging corner taken from the left by-line by Jean Beausejour, clearance made by Per Mertesacker.
Ronnie Stam delivers the ball, Per Mertesacker makes a clearance. Inswinging corner taken left-footed by David Jones, Kieran Gibbs manages to make a clearance. Effort on goal by Maynor Figueroa from 35 yards went harmlessly over the net.
Bacary Sagna challenges Maynor Figueroa unfairly and gives away a free kick. Free kick taken by Maynor Figueroa.
Free kick taken by Wojciech Szczesny.
Substitution Lukas Podolski goes off and Francis Coquelin comes on.
Callum McManaman is flagged offside by the assistant referee.
A cross is delivered by Ronnie Stam.
Substitution Callum McManaman joins the action as a substitute, replacing Franco Di Santo.
Theo Walcott has an effort direct from the free kick.
Substitution (Arsenal) makes a substitution, with Aaron Ramsey coming on for Alex Oxlade-Chamberlain.
Maynor Figueroa concedes a free kick for a foul on Lukas Podolski.
The ball is delivered by Alex Oxlade-Chamberlain, clearance by Ronnie Stam.
Jean Beausejour crosses the ball. David Jones has an effort at goal from just outside the box which goes wide of the right-hand post.
Kieran Gibbs sends in a cross, save made by Ali Al Habsi.
Alex Oxlade-Chamberlain takes a shot. James McArthur gets a block in. Corner taken by Theo Walcott from the left by-line played to the near post, clearance by David Jones.
Unfair challenge on Santi Cazorla by David Jones results in a free kick. Free kick taken by Mikel Arteta.
Arouna Kone takes a shot. Save by Wojciech Szczesny.
Shot from 25 yards from Maynor Figueroa. Save made by Wojciech Szczesny.
Jean Beausejour delivers the ball, clearance made by Per Mertesacker. Outswinging corner taken left-footed by Jean Beausejour, clearance made by Bacary Sagna.
Theo Walcott is ruled offside. James McCarthy takes the indirect free kick.
Shaun Maloney takes a short corner. The ball is swung over by Jean Beausejour, save by Wojciech Szczesny.
Centre by Shaun Maloney, blocked by Per Mertesacker.
Franco Di Santo is flagged offside by the assistant referee. Wojciech Szczesny takes the indirect free kick.
Jack Wilshere is adjudged to have handled the ball. Free kick taken by James McArthur.
The assistant referee signals for offside against Ronnie Stam. Wojciech Szczesny restarts play with the free kick.
A cross is delivered by Alex Oxlade-Chamberlain, clearance made by Maynor Figueroa.
The ball is delivered by Jean Beausejour, Bacary Sagna gets a block in.
Franco Di Santo concedes a free kick for a foul on Kieran Gibbs. Free kick taken by Kieran Gibbs.
Thomas Vermaelen fouled by Arouna Kone, the ref awards a free kick. Kieran Gibbs takes the direct free kick.
Foul by Shaun Maloney on Mikel Arteta, free kick awarded. Mikel Arteta restarts play with the free kick.
Jean Beausejour produces a left-footed shot from just outside the box that misses to the right of the goal.
59:14 Goal scored
Goal! - Mikel Arteta - Wigan 0 - 1 Arsenal Penalty taken right-footed by Mikel Arteta and scored. Wigan 0-1 Arsenal.
Theo Walcott fouled by Jean Beausejour, the ref awards a Penalty. Assist on the goal came from Theo Walcott.
Kieran Gibbs delivers the ball.
The ball is crossed by Jack Wilshere, Maynor Figueroa makes a clearance.
The ball is delivered by Alex Oxlade-Chamberlain, clearance made by Maynor Figueroa.
Jean Beausejour delivers the ball, Kieran Gibbs manages to make a clearance. Shaun Maloney is penalised for handball and concedes a free kick. Wojciech Szczesny restarts play with the free kick.
The ball is crossed by Alex Oxlade-Chamberlain.
Foul by Ronnie Stam on Santi Cazorla, free kick awarded. Lukas Podolski restarts play with the free kick.
Alex Oxlade-Chamberlain fouled by James McArthur, the ref awards a free kick. Shot on goal comes in from Lukas Podolski from the free kick.
Effort from a long way out by Maynor Figueroa goes wide left of the goal.
Kieran Gibbs challenges Franco Di Santo unfairly and gives away a free kick. Ali Al Habsi restarts play with the free kick.
Alex Oxlade-Chamberlain crosses the ball, Theo Walcott takes a shot. Ali Al Habsi makes a save.
A cross is delivered by James McCarthy, Thomas Vermaelen manages to make a clearance.
The ball is crossed by Bacary Sagna, blocked by Jean Beausejour.
The ball is crossed by Alex Oxlade-Chamberlain, clearance by Emmerson Boyce.
The match restarts for the second half.
45:00 +2:12 Half time
Half Time It is the end of the first-half.
Free kick awarded for an unfair challenge on Jack Wilshere by Shaun Maloney. Direct free kick taken by Mikel Arteta.
Free kick awarded for a foul by Kieran Gibbs on Ronnie Stam. Direct free kick taken by Ronnie Stam.
Shot by Franco Di Santo from outside the box goes over the target.
David Jones takes the direct free kick.
Booking Jack Wilshere is cautioned by the ref for unsporting behaviour.
Free kick awarded for an unfair challenge on Shaun Maloney by Jack Wilshere.
Outswinging corner taken right-footed by Theo Walcott from the right by-line.
The referee blows for offside against Jean Beausejour. Indirect free kick taken by Wojciech Szczesny.
The referee penalises Shaun Maloney for handball. Mikel Arteta takes the direct free kick.
Theo Walcott takes a shot. Blocked by Emmerson Boyce.
Unfair challenge on Mikel Arteta by David Jones results in a free kick. Per Mertesacker takes the direct free kick.
Jean Beausejour produces a cross.
Foul by Jean Beausejour on Alex Oxlade-Chamberlain, free kick awarded. Mikel Arteta delivers the ball from the free kick right-footed from right wing, Emmerson Boyce manages to make a clearance.
Effort on goal by Arouna Kone from inside the box misses to the right of the target.
James McCarthy fouled by Bacary Sagna, the ref awards a free kick. Maynor Figueroa restarts play with the free kick.
The referee gives a free kick against Jean Beausejour for handball. Free kick taken by Wojciech Szczesny.
Theo Walcott takes a shot. Maynor Figueroa gets a block in.
Lukas Podolski challenges Franco Di Santo unfairly and gives away a free kick. Franco Di Santo restarts play with the free kick.
Lukas Podolski produces a left-footed shot from the edge of the box and misses to the left of the target.
Unfair challenge on Mikel Arteta by James McArthur results in a free kick. Free kick taken by Mikel Arteta.
Shot by Mikel Arteta. Maynor Figueroa gets a block in.
Lukas Podolski produces a drilled left-footed shot from 20 yards. Ali Al Habsi makes a save.
Effort on goal by Arouna Kone from 20 yards. Wojciech Szczesny makes a comfortable save.
Shot by Alex Oxlade-Chamberlain. Ali Al Habsi makes a save. Outswinging corner taken by Theo Walcott from the right by-line, James McArthur manages to make a clearance.
The assistant referee signals for offside against Arouna Kone. Free kick taken by Wojciech Szczesny.
A cross is delivered by Franco Di Santo, clearance made by Thomas Vermaelen.
Santi Cazorla challenges David Jones unfairly and gives away a free kick. Ali Al Habsi takes the free kick.
Theo Walcott takes the outswinging corner, James McCarthy makes a clearance.
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