Owen Coyle's side should have been more than two ahead at half-time and there were a few nervy moments after the visitors pulled one back but a late goal from Nick Powell made it 3-1.
Roberto Martinez, the man who led the Latics to their unlikely FA Cup triumph last season, watched on from the directors' box as his former side made another piece of history.
After the Latics' 0-0 draw with Zulte Waregem in Bruges two weeks ago, the honour of first European goalscorer for the club was still up for grabs.
And it went to Powell in the 21st minute, although the on-loan Manchester United midfielder owed a major debt of thanks to Maribor keeper Jasmin Handanovic.
Jean Beausejour's deflected cross did not look likely to cause any danger but Handanovic inexplicably punched the ball behind him for Powell to nod into an empty net.
Beausejour had more of an intentional hand in the second goal 34 minutes in, sending in a superb cross that left cup final hero Ben Watson the simple task of heading past Handanovic.
The hosts should have been out of sight before Maribor captain Tavares pulled a goal back on the hour mark, but Powell made sure with an individual effort in injury time.
The result left Wigan well positioned on four points in Group D, two behind Rubin Kazan, who hammered Zulte 4-0 earlier on Thursday and who the Latics play home and away next.
Maribor are the reigning Slovenian champions but have been in poor form, which cost manager Ante Cacic his job at the weekend with Ante Simundza swiftly replacing him.
A new-look Wigan have made a steady start to life back in the Championship, winning three of their first eight games, but juggling the demands of the league and a European campaign has already caused Coyle to complain about fixture congestion.
Injuries have not helped and Coyle was again without a recognised striker as Grant Holt and Marc-Antoine Fortune joined five other senior players on the sidelines.
Powell lined up through the middle, with Jordi Gomez pushing on to support him from midfield and Callum McManaman and Beausejour out wide.
The home side made a bright start, playing at a high tempo, and they really should have been ahead in the eighth minute.
A misplaced pass from Maribor played Powell clean through but his poked shot was deflected just past the post by Handanovic.
From the corner, the ball fell to James McArthur on the edge of the area, who fired just wide.
It took Maribor 18 minutes to manage a shot on Scott Carson's goal, which was deflected behind, and when the corner was cleared Ales Mejac let fly from 30 yards.
Carson looked beaten but to his relief the ball whistled just past the post.
From the goal kick Wigan resumed their pursuit of a goal, which duly arrived thanks to Handanovic's moment to forget.
Frenchman Jean-Philippe Mendy had been earmarked as a threat to the Latics and he twice fired in shots as Maribor sought a response but both times Carson was comfortably behind them, and soon it was 2-0 to the hosts.
The only concern for Coyle at half-time would have been that his side had not scored more.
Powell was again played through by a Maribor error but chose an ambitious chip that cleared the bar when he could have taken the ball on or played in an unmarked McArthur.
Beausejour then scuffed his shot when well placed at the far post and McManaman drilled just wide.
The pattern of the game remained the same at the start of the second half, and Powell was guilty of another bad miss in the 55th minute.
McArthur played in Beausejour, whose cross looked on a plate for the midfielder but he was stretching and somehow managed to hit a post from five yards out in front of an unguarded net.
And the misses looked very costly five minutes later when Mendy held off Ryan Shotton to run into the area and pull the ball back for Tavares.
Now it was the visitors looking the more settled and there was an air of nervousness around the DW Stadium which was not helped when Powell again came agonisingly close, this time Watson's cross just evading him.
As the clock ticked towards 90 minutes, Tavares threatened again but was denied a spectacular goal by a fine save from Carson.
And moments later Powell at last grabbed his second, jinking through the Maribor defence and this time comfortably beating Handanovic.
It could have been four, but with the final effort of the match Leon Barnett saw his shot cleared off the line.