Nick Powell was the man to make history for Latics as he scored the club's first goal in European competition, following it up with a second in second half injury time after Ben Watson had made it 2-0 in the first half, but with Maribor's Brazilian forward making it 2-1 on 59 minutes.
Latics were made to work hard for the points in the second half, but they created a plethora of chances, with Powell hitting the post and Leon Barnett having a late chance for 4-1 blocked at the last second.
The victory puts Latics second in Europa League group D on four points.
Owen Coyle made three changes to the team that started the weekend's Championship game against Watford, with Emmerson Boyce, Jean Beausejour and Callum McManaman coming in for Thomas Rogne, James McClean and Marc-Antoine Fortune.
From the moment the players walked out onto the pitch to the Europa League theme music the supporters were filling the stadium with noise, as chants of "FA Cup Champions" rang loud and clear.
Latics made a bright start to the game with a series of free kicks earned in Maribor's defensive third.
Powell should have arguably scored Latics' first European goal after just seven minutes when a back pass allowed him to race through one-on-one with Jasmin Handanovic, but the keeper made Powell wait until the 21st minute for his golden moment, as he made a smart save on this occasion.
The opening exchanges were dominated by Latics' possession as Maribor stepped off and allowed space.
More free kicks were given away by the Slovenian Champions, with Latics coming closer and closer as Jordi Gomez fired a free kick into the face of a defender in the Maribor wall.
Moments later Powell made Wigan Athletic history as from the throw-in that followed Gomez free kick, Jean Beausejour played in a teasing cross towards the goalkeeper.
Handanovic went to punch, but it went horribly wrong for the 'keeper as the ball spun off his fist, behind his head and onto the head of the prowling Powell who nodded the ball into an empty net.
More and more pressure either side of a couple of simple saves from Scott Carson followed, before Ben Watson doubled Latics' lead with another headed goal.
Now a dangerous asset in the air following his FA Cup heroics, Watson leaped to reach a bending Beausejour cross from the left just before the 'keeper, with the net bulging and Latics' supporters going into a frenzy.
With confidence oozing through the team, Powell almost added a second with a cheeky chip, Beausejour then came close at the back post as he got on the end of a Callum McManaman cross, and then the winger himself flashed a low drive just beyond the left post as he cut inside from the right.
The early stages of the second half proved a little more tricky for the hosts as Maribor got a goal back, but not before Powell hit the post from close range as he dove to meet another brilliant ball in by Beausejour.
Latics were forced to concentrate when Maribor made it 2-1 as Jean-Philippe Mendy raced through on goal in a battle with Ryan Shotton, cutting the ball back into the area for Tavares to follow in.
It created a sense of discomfort for a brief spell, but Latics upped their game again, with Powell once more finding space at the back post as he came inches away from connecting with a Watson cross.
With just three saves to make during the game from Maribor half chances, Scott Carson was called into action in the 90th minute as he looked to have saved Latics three points when he tipped a fierce Tavares drive over the bar.
A minute later Powell repaid his goalkeeper's work with a sublime second goal.
Jinking in from the right side he dribbled beyond two defenders before sliding the ball past an outstretched Handanovic.
The stadium was again a cauldron of noise as the supporters saw three points edging closer and closer, but it could have been more in the final blows of added time as Latics broke three on one, with substitute Nouha Dicko sprinting from the half way line to set up Leon Barnett, but a last minute block kept the score at 3-1.
As the referee blew his final whistle Latics created yet more history in 2013 as they sealed three points in Europe for the first time, the full time score Latics 3 Maribor 1.