Jordi Gomez scored from the spot to complete the Latics' second away comeback in a row after Steven Reid and Victor Moses had scored great first-half goals
Gomez coolly slotted home after Victor Moses had been tripped by Steven Reid in the penalty area.
Both players had earlier scored their first goals of the seasons with Reid scoring from a free-kick before Moses equalized with a curled effort into the top corner.
West Brom pushed for an equalizer but despite having several opportunities they could not find the back of the net.
Wigan almost found itself a goal down early on when Chris Brunt got on to the end of Jerome Thomas’s cross but could only volley over. Brunt then hit a thunderbolt from 20 yards against the bar with Ali Al Habsi beaten after a West Brom free-kick was cleared straight to him.
The Latics soon got a grip on the game with their 5-4-1 formation stifling any further attacks, before gradually beginning to threaten more going forward as first Victor Moses shot wide from distance and then a scramble in the West Brom penalty saw Ben Foster just get to the ball before Connor Sammon after tackles from three Baggies defenders.
The game was needing some inspiration and it got is after the half-hour mark. Caldwell was penalized for a shirt tug on Odemwingie by the linesman much to his annoyance and from 25 yards out Reid curled it over the wall and into the top right-hand corner with Al Habsi rooted to the spot.
However, minutes later Wigan was level and it was another great strike, this time from Moses. Diame’s cross from the left bounced off Mulumbu who was sliding in to try and clear the ball only to fall to the winger who opened his body up to curl a beautiful shot into the far corner to score his first goal for 13 matches since his goal against the same opposition last season.
West Brom went behind as for the fourth home game in a row as it conceded a penalty, this time Gomez was the beneficiary as he sent Al Habsi the wrong way from the spot.
The home side, stunned by Wigan’s goal, pressed forward for an immediate response but despite putting several dangerous crosses into the area, it was unable to find a way past Al Habsi who repeated his heroics from his last time in the Midlands against Wolves by saving a Long header at his near post.
Both sides had opportunities in the final third but neither could make the final ball count. Despite having a late free-kick, West Brom, which has the worst home record in the league, could not salvage a point.