Leon Barnett put the hosts ahead early on, brilliantly volleying home from the edge of the penalty area after a Jordi Gomez miscue.
An open first half ended even, though, young Wigan goalkeeper Lee Nicholls spilling an effort from Thorgan Hazard over his own goal line.
Wigan looked like the only team likely to score in the second period, but Junior Malanda slammed home an 88th-minute winner to move the Belgians second in Group D with one game to play.
The Championship side must win at Maribor in their final game, while hoping Waregem lose at runaway group winners Rubin Kazan, although the Slovenian champions remain in the hunt themselves.
Owen Coyle made six changes from Saturday's 1-0 defeat to Brighton and Hove Albion, Manchester United loanee Nick Powell starting at the head of Wigan's attack with Gomez supporting. Waregem came into the clash on the back of a six-game unbeaten run but still made three alterations from their weekend win over Mechelen.
The hosts were ahead after just seven minutes as Callum McManaman and Gomez worked a short corner routine, only for the Spaniard to mis-hit his effort. However, the ball fell perfectly for Barnett, who slammed home his fourth goal of the season.
Within 10 minutes of the opener, McManaman almost doubled the lead and Waregem midfielder Sven Kums scuffed wide after electric build-up play from Frederic Duplus on the left.
James McClean ended a strong run with a shot from the left channel that visiting keeper Sammy Bossut saved well, although the Irishman had better options centrally.
And Bossut's sharpness was rewarded in part through an error by his opposite number as the visitors pounced on an error from James McArthur to drive up the field.
The ball eventually found Hazard, whose firm effort was straight at Nicholls, but the 21-year-old was caught in two minds and could only drop the ball over the line.
Powell stung Bossut's palms with a well-struck shot on the hour, while Nicholls reacted well to palm Hazard's deflected free-kick behind eight minutes later as the sides firmed up after the break.
McArthur drilled a 20-yard shot wide with 10 minutes on the clock as the hosts pushed for a winner that looked as though it would fail to materialise.
But Malanda got on the end of fellow substitute Idrissa Sylla's cutback and lashed an unstoppable effort past Nicholls to deflate the home crowd and put Waregem in the driving seat for a spot in the next phase.
