Athletic remain third in the division, but they are now one point adrift of Shrewsbury Town in second and two off leaders Blackburn Rovers, with two games in hand to play on both of their automatic promotion rivals.
The hosts were looking to climb clear of the drop in Dean Keates's first match in charge, but they were nearly behind inside a minute as Dunkley powered a header wide.
Nick Powell, back to full fitness after starting the FA Cup quarter-final defeat to Southampton on the bench, then headed over from a good position after Ryan Colclough hooked the ball into a dangerous position.
Walsall, now beaten in five of their last six, enjoyed a good spell prior to going a goal down - Dunkley being needed to keep out a shot from Amadou Bakayoko.
Wigan were soon on their way, though, with Jacobs turning in Powell's cross for the opener - and his 50th goal in professional football - with just over half an hour on the clock.
Fulton doubled the visitors' tally with his first strike for the club, firing low into the bottom corner from distance, before Dunkley tapped in from closer range once Liam Roberts dropped a corner.
Maziar Kouhyar and Kieron Morris both came close to responding for the Saddlers, the latter forcing Christian Walton into a low save, while Bakayoko came out second best when up against the Wigan keeper.
The remainder of the match saw Athletic retain possession and see things through with minimal fuss, with Colclough firing wide from the last of the chances.
WALSALL (4-2-3-1): Roberts; Devlin, Fitzwater, Guthrie, Leahy; Chambers, Dobson (Cuvelier 70'); Morris, Kouhyar, Oztumer; Bakayoko
WIGAN ATHLETIC (4-2-3-1): Walton; Byrne, Dunkley, Burn, Elder; Power, Fulton (Roberts 82'); Colclough, Powell, Jacobs (Cole 89'); Vaughan (Grigg 70')