Callum McGregor tapped the visitors into a sixth-minute lead after good work from Stefan Johansen.
Nevertheless, the Slovenian outfit responded well and hit back through Damjan Bohar on 14 minutes as both sides cancelled each other out.
Below, you can relive all of the action with Sports Mole's live commentary.
Maribor: Handanovic; Suler, Rajcevic, Viler, Filipovic; Ibraimi, Dervisevic, Vrsic, Stojanovic; Bohar, Tavares
Celtic: Gordon; Lustig, Denayer, van Dijk, Izaguirre; McGregor, Mulgrew, Kayal, Johansen, Berget; Stokes
Aalborg 1-0 Apoel Nicosia
Lille 0-0 Porto
Slovan Bratislava 0-1 Bate Borisov
Standard Liege 0-1 Zenit