The visitors came from behind to lead at half-time as Davy de Fauw's early goal was cancelled out by Matic Crnic and Ales Mertelj volleyed a superb second.
Dejan Mezga extended the lead and although Martin Milec was sent off shortly afterwards, Zulte were unable to find a way back into the game.
Maribor's Marcos Tavares had an early shot saved before his side fell behind in the 12th minute.
Thorgan Hazard fired a left-wing free-kick straight at goal, keeper Jasmin Handanovic fumbled and Zulte captain De Fauw followed up to score.
But the lead lasted just eight minutes as Steve Colpaert was caught in possession and Crnic sent a long-range shot swirling past the helpless Sammy Bossut.
Mertelj shot wide while at the other end, Handanovic made a better job of fielding another Hazard shot.
But Maribor took the lead when Mezga's corner was cleared but the ball dropped perfectly for Mertelj to send a looping 20-yard volley into the top corner.
Jean-Philippe Mendy headed another Mezga corner wide while Mertelj and Zulte's Habib Habibou were off target in stoppage time.
Zulte boss Francky Dury sent on Raphael Caceres and Idrissa Sylla for Frederic Duplus and, surprisingly, Hazard at half-time.
But it was to no avail as Mezga put Maribor 3-1 up just four minutes after the restart, sidefooting home via a post after Tavares cut the ball back.
The Belgians were unexpectedly handed a way back into the game, though, when Milec collected two bookings in the space of three minutes for fouls on Habibou and was dismissed.
Handanovic saved from De Fauw and Sylla, though, and defender Karel D'Haene shot over from close range.
Further chances went astray for Sylla and Habibou before Mendy had an opportunity to ease Maribor's nerves, only for Sammy Bossut to save.
Caceres fired against the post in injury time but Zulte were kept at bay.