The winner could progress to the round-of-32 if Belgian side Zulte Waregem, who sit second, lose at Group D winners Rubin Kazan.
Maribor go into the encounter with four points from their first five matches, while Wigan sit a place above with one more point, despite losing their past two in the competition.
Wigan's preparation for the trip to Slovenia has not been ideal, with new manager Uwe Rosler only appointed as Owen Coyle's successor on Saturday and the German is determined to give the tie his full attention.
He said: "I know Sunday (against Bolton) is a massive game and I have to be sensible, especially when you have players coming back from injury.
"But when you lose five games in a row your first priority is to start winning football games. So, we will have a competitive team in Maribor. We owe it to ourselves and to the fans who are travelling down there.
"We have to embrace the competition because you never know when Wigan will play in Europe again. We have to get out of this habit of losing games and we have to change that momentum as soon as possible.
"I have a very talented squad of players, I'm looking to play a 4-3-3; the players are very familiar with the formation from the past, from Roberto (Martinez).
"Every player can show themselves now until the transfer window opens, everyone can impress."
History does not offer Maribor much inspiration as they have never beaten an English team in Europe, playing five times and losing four.
The most recent English club they faced was Birmingham City, and they – like Wigan this season – had just been relegated from the Premier League.
Maribor's form in the competition going into the match is poor after losing three and drawing one of their past four games, but Wigan's inability to score a goal away from home in Europe gives them hope.
The Slovenian First Football League leaders have no pressing injury concerns and were able to name a strong side in their 1-0 weekend win over Rudar.
Rosler confirmed that he would be resting striker Grant Holt for the derby with Bolton, and winger James McClean will be suspended after picking up three yellow cards.
