Teenager Nick Powell scored in either half, including the club's first goal in European competition, sandwiching an effort from Ben Watson. Marcos Tavares had pulled one back for the Slovenians before the Manchester United loanee doubled his tally but the Latics fully deserved their victory.
The Championship outfit climbed to second in Group D with the three points, while their visitors remain pointless at the foot of the standings.
Manager Owen Coyle made three changes to the Wigan side that lost 1-0 to Watford on Saturday, with experienced duo Emmerson Boyce and Jean Beausejour coming in to the mix. The 47-year-old was unable to call on seasoned striker Marc-Antoine Fortune, though, after the 32-year-old limped off last weekend, with youngster Callum McManaman drafted in.
|VIEW FROM THE DW STADIUM
|By Tom Marshall-Bailey
This European lark appears to be a walk in the park for Wigan, who dispatched a desperately disappointing Maribor side like seasoned veterans in this competition, providing a welcome boost ahead of a daunting double header against Russian outfit Rubin Kazan.
Following on from a creditable away draw with Zulte Waregem in September, the Latics secured a maiden win at this level as Nick Powell and Ben Watson teamed up to see Owen Coyle's men to victory.
Sure, they were helped by the abysmal goalkeeping display of Jasmin Handanovic - who presented the hosts with their two first-half goals - but take nothing away from Wigan, as they held off the attentions of Maribor in the second period to pull through and secure a win that could ultimately prove crucial in their quest to escape the group stage and get a taste for the knockout stage.
It was the home side who started brightest, with 19-year-old Powell going one-on-one with goalkeeper Jasmin Handanovic in the seventh minute only to see his attempted lob well saved by the Slovenian.
The visitors spurned a fine opportunity of their own 10 minutes later, as Goran Cvijanovic shot wide when well placed on the edge of the box, and he was made to rue his missed chance soon afterwards as Powell pounced on a poor clearance from Handanovic to sweep home the loose ball with 22 minutes gone.
The hosts doubled their lead 11 minutes before the interval when Beausejour's superb cross was headed in by midfielder Watson.
The start of the second half saw the visitors get more of a foothold in the game but they still left Scott Carson untested and it was Wigan who looked more likely to add to their tally.
Powell almost grabbed his second in the 54th minute but his effort from Beausejour's delivery struck the post and, just five minutes later, Maribor reduced the deficit after good work from Jean-Philippe Mendy was rewarded by Tavares's confident close-range finish.
Simundza made three late changes in an attempt to rally his side to an unlikely comeback but, after Carson had clawed away Tavares's powerful strike, Powell did net his second, darting past three players before coolly beating the keeper.