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Legia Warsaw had beaten the Hoops 6-1 on aggregate in the third qualifier but were effectively dumped out of the competition by UEFA for bringing on a player who should have been suspended in the second leg at Murrayfield, which left Ronny Deila's side facing the Slovenian champions.
Callum McGregor shot the visitors into the lead in the sixth minute, only to see his fourth goal in seven games cancelled out by Damjan Bohar.
Hoops skipper Charlie Mulgrew and defender Virgil van Dijk came close before the interval as the Scottish champions showed a marked improvement on their Legia performances.
Maribor came out with more purpose at the start of the second half in the Ldjuski vrt stadium but the Hoops held firm and indeed Stefan Johansen passed up a great chance to win the game when he stumbled when he was right through - but nevertheless they are in the box seat going into the second leg at Celtic Park next Tuesday.
Hector Herrera scored the only goal as Porto left France with a 1-0 victory over Lille.
Despite playing away from home, Porto had 60 percent of the possession, and controlled most of the first half. The hosts exerted themselves a little more to open the second half but it was the away side that took the lead in the 61st minute.
Lille keeper Vincent Enyeama did well to keep out Barcelona loanee Cristian Tello's shot but could not stop Herrera from tapping home the winner.
Lille's best chance to score came in the 76th minute when Porto goalkeeper Fabiano spilled a Sebastien Corchia free kick, but Maicon was there to clear.
Oleg Shatov's first-half goal gave Zenit St Petersburg a 1-0 win, and a crucial away goal, as the Russian side triumphed against Standard Liege in Belgium.
Shatov rounded off a fine move to make the game's only breakthrough after 16 minutes when he sidefooted home after excellent build-up play involving Domenico Criscito, Danny and Hulk.
Standard produced an improved second-half display but were thwarted by goalkeeper Yuri Lodygin, who made fine stops to deny Tony Watt and -- with less than 10 minutes remaining -- Jeff Louis, to preserve the lead for Andre Villas-Boas and his side.
Cypriot club APOEL hold a slim advantage after holding Danish side Aab to a 1-1 draw in Aalborg.
The hosts took a lead in the 16th minute when Patrick Kristensen threaded a pass through an APOEL defender's legs for Nicolaj Thomsen to finish into the far corner.
APOEL's Brazilian midfielder Vinicius scored from eight yards to equalise nine minutes into second half and his club were happy to play out the rest of the match and return to Cyprus with an away goal in hand.
Slovan Bratislava salvaged a 1-1 draw at home to BATE Borisov to keep their hopes alive.
Tomas Jablonsky's own goal had given the Belarussians the advantage just before the break, but Slovakia striker Robert Vittek hit back 10 minutes from time.