Celtic, who were reinstated to Europe's premier club competition after Poland's Legia Warsaw were punished for fielding an ineligible player, made a bright start against the Slovenian champions when Callum McGregor gave them a sixth-minute lead.
McGregor, enjoying a fine start to his debut season with the Glasgow giants, pounced on a rebound after Jo Inge Berget was initially denied by Maribor goalkeeper Jasmin Handanovic to fire home his fourth goal in seven matches
However, Ronny Deila's men were pegged back just before the quarter-hour as Zeljko Filipovic thread the ball through to Damjan Bohar who held his composure to calmly steer beyond Celtic 'keeper Craig Gordon.
Filipovic then came to his side's rescue to clear Charlie Mulgrew's header off the line before Celtic midfielder Stefan Johansen unwittingly got in the way of team-mate Virgil Van Dijk's goalbound effort.
Maribor, whose lone appearance in the Champions League group stage came 15 years ago, kept Gordon on his toes with a pair of long-range attempts with Celtic proving far more resolute defensively than they were in the previous round against Legia.
Johansen squandered a golden chance to put the Scottish champions in the driving seat midway through the second half as he lost his balance having escaped clear of the Maribor defence but Celtic will remain confident of completing the job in Tuesday's return leg at Parkhead.
"I think we were closer to winning the game than they were," Celtic boss Deila told SkySports afterwards.
"The performance was good, I'm pleased and it's going to be very exciting to play them at Celtic Park next week."
Two-time former European champions Porto will take a 1-0 advantage into next week's second leg against Lille in Portugal.
Mexico international Hector Herrera popped up with the game's lone goal on 61 minutes at the Stade Pierre-Mauroy to leave Porto on the cusp of a fourth straight group stage appearance.
Oleg Shatov's 16th-minute strike put Zenit St Petersburg in control of their tie as Andre Villas-Boas' men secured a 1-0 win at Belgium's Standard Liege.
Slovan Bratislava striker Robert Vittek equalised 10 minutes from time in a 1-1 draw at home to Belarusian outfit BATE Borisov to leave the Slovak title-holders in with a fighting chance of the reaching the group stage for the first time.
APOEL Nicosia, surprise quarter-finalists in the 2011-12 competition, secured a vital away goal courtesy of Brazilian midfielder Vinicius as the Cypriot champions recovered to earn a 1-1 draw at Danish side Aalborg.
Source : AFP
Source: AFP