The Latics continued to dominate but were unable to add a second before Stoke got back on level terms four minutes before the interval.
Martin Atkinson again pointed to the spot for handball and this time it was Maynor Figueroa who was penalised, with Jonathan Walters applying the finish from 12 yards to send the sides in level at the break.
The scoreline didn't stay at one apiece for long, as Wigan retook the lead four minutes into the second 45 when Arouna Kone held the ball up well before teeing up strike partner Franco di Santo to stroke home.
Stoke then took hold of the game and eventually netted the fourth of the game when Walters sent over a cross that Peter Crouch headed in.
Both teams rise in the table, with Wigan moving up to seventh and Stoke climbing to tenth.