The hosts never stopped pushing for a winning goal but could not break down a determined Burnley rearguard.
The closest they came was in the first half when former Claret Chris McCann's header was cleared off the line.
High-flying Burnley had chances of their own, and almost nicked what would have been a winning goal on the stroke of half-time.
Kieran Trippier's pull-back was lashed goalwards by ex-Wigan man David Jones. Goalkeeper Ali Al Habsi touched the ball on to the bar and was grateful to see Leon Barnett clear with Danny Ings sniffing around.
Wigan, looking to get back to winning ways after the Boxing Day stalemate, looked bright from the outset and Stephen Crainey's free-kick caused concern in the Burnley ranks.
Barnett got his head to the ball but could only direct it behind for a goal-kick.
The Latics came closer still when a corner from the left found McCann 12 yards from goal, but the Irish midfielder's effort was cleared off the line and hacked away to safety.
Jordi Gomez fed Marc-Antoine Fortune, whose shot was parried by Tom Heaton with Nick Powell - back after injury - ready to capitalise.
At the other end, Sam Vokes fired high and wide from close range, with the same player then forcing the first save of the game from Al Habsi.
Michael Duff picked up the game's first yellow card for a lunge on James McArthur, but the free-kick from Gomez fizzed just past the post.
The Latics threatened again when Barnett's searching cross towards the far post was met by the head of James Perch, but the defender's effort flashed past the far post with the goalkeeper beaten.
Powell did well to turn his marker but his shot was off the mark, before McCann led a three-on-three break just before the interval.
McCann was tripped by Duff at the expense of a free-kick, which came to nothing.
And the Clarets came agonisingly close to opening the scoring in first-half stoppage-time when Trippier raced to the byline in acres of space.
The right-back's pull-back found Jones, whose right-foot strike seemed destined for the top corner before Al Habsi touched it on to the bar.
The ball then bounced off the back of Al Habsi and looked as though it might sneak over the line, before Barnett booted clear in the nick of time.
Wigan started the second period on top and Powell fed McCann, whose shot was well over the top.
James McClean took over from Fortune for the hosts, with Powell moving up to centre-forward.
And Powell became the second name in the book for an incident with Jason Shackell.
Ings fired wide for Burnley, with McCann's effort for Wigan being well blocked by a defender.
Both teams made changes in the final stages, Roger Espinoza for Wigan and Michael Kightly for Burnley.
Powell fired Wigan's last effort into the side-netting, while Burnley had half a claim for handball against Ivan Ramis turned down.