The Belgian side eased into a two-goal lead thanks to strikes by Vadis Odjidja in the seventh minute and Nabil Dirar in the 24th and were never troubled by their Slovenian opponents, who had Aleksander Rajcevic dismissed late on.
The hosts took an early advantage as Odjija showed good skill to outfox the visiting defence before netting.
Brugge looked to press home their advantage and Odjija fired a free-kick over the bar after Ales Mejac fouled Lior Rafaelov 20 yards out.
They created another chance after 17 minutes as Joseph Akpala sent Dirar's cross over, before Maribor had an attempt of their own, which Dejan Mezga put over from 20 yards.
Brugge gave further warning of their danger when Odjija's fine effort was parried clear by Jasmin Handanovic after 22 minutes.
Two minutes later they had doubled their lead as Dirar powered the ball home from inside the box.
After 36 minutes Dirar was involved again as he crossed for Joseph Akpala, who could not divert the ball goalwards.
Maribor had a rare chance in the 39th minute when, from a free-kick, Dalibor Volas teed up Marcos Tavares, whose strike went over.
Akpala came close to making it 3-0 in the 40th minute when he turned a cross from Carl Hoefkens into the arms of Handanovic.
Maribor had another chance before the break but Lior Rafaelov could not find the target with a free-kick from the edge of the box.
The hosts were in cruise control after the break, with Hoefkens and Dirar having shots blocked before Hoefkens headed a corner from Victor Vazquez over.
Mejac curled a Maribor chance over after 63 minutes, but it was Brugge who came closest to scoring again when Ryan Donk's header from Jonathan Blondel's corner was parried clear by Handanovic.
A miserable night for Maribor was complete five minutes from time when Rajcevic brought down Akpala and was dismissed for a professional foul.