After a frenetic first half low on quality, Theo Walcott and Santi Cazorla provided the breakthrough to enable the Spaniard to slot home from the spot and hand his side victory
The Spanish midfielder sent Ali Al Habsi the wrong way from the spot on 60 minutes following Jean Beausejour's clumsy foul on Theo Walcott after neat work between the England striker and Santi Cazorla.
Wigan was the better team for long spells, but wasteful crossing from the wings and poor finishing from Aroune Kone left the Latics frustrated and winless in five league games.
Arsene Wenger gave Walcott was given his preferred starting role up front backed by Alex Oxlade-Chamberlain, Cazorla and Lukas Podolski.
Wigan won 2-1 at the Emirates the last time the sides met and showed no fear in the first half, but it was Arsenal which had the first real chance.
Cazorla turned James McArthur easily and found Mikel Arteta in space. The Spaniard fed Oxlade-Chamberlain on the right, who forced Ali Al Habsi into a fine one-handed stop from 16 yards.
Wigan should have taken the lead after 24 minutes as Di Santo put Kone clean through on goal, but with just Wojciech Szczesny to beat, the Ivory Coast striker dragged his shot wide from eight yards.
The second half began much as the first with both teams breaking forward looking for an early goal, and Al Habsi was forced into a great stop on 48 minutes. Oxlade-Chamberlain found space on the right wing and pulled the ball back for Walcott, whose finish was close enough for the Wigan keeper to get down to and tip away well.
However, the game turned with half an hour to go as Arsenal found the breakthrough, with the danger again coming from the right.
Walcott and Cazorla's link-up play on the wing was too intricate for Beausejour, and referee Jonathan Moss blew for a penalty as the striker was felled by the defender. Arteta found the bottom left-hand corner of Al Habsi's net with his penalty kick.
Wigan kept coming though, and Kone did well to work the ball from the left before forcing a fine low stop from Szczesny with 20 minutes remaining, while Jones could only crack an effort narrowly wide two minutes later.
Mertesacker had to be alert to deny Kone late on in the area, while McArthur dragged a shot wide late in injury time as Wenger's side saw the game out for a much-needed victory.