Maribor grabbed the second place in qualifying Group D from Zulte Waregem as the Belgian side lost to Russia's Rubin Kazan in the other match of the group 0:2 at home.
Wigan scored the first goal of the match in the 41st minute, pushing the Slovenian champions on the brink of elimination from Europe's second-strongest club football competition.
Dejan Mezga equalled the score in the 43rd minute and Željko Filipović put Maribor ahead 2:1 in the 59th minute, scoring what later turned out to be the winning goal.
Maribor also needed Rubin Kazan, who have already advanced to the second round, to win in Belgium. And win they did, beating Zulte Waregem 2:0 with two late goals.
This is Maribor's second biggest success in Europe, following the qualification to the UEFA Champions League in the 1999/2000 season.
The draw for the knock-out stage will be held on 16 December. The first legs will be played on 20 February, and the second legs on 27 February 2014.