The midfielder scored in the sixth minute as Ronny Deila's men escaped Slovenia with a creditable result, while there were also wins for Zenit and Porto in other ties
The Scottish champions are only participating in the play-off round after they were reinstated by Uefa following Legia Warsaw's sanction for fielding an ineligible player at the third qualifying stage.
And Ronny Deila's men will be satisfied with a draw against Slovenian champions Maribor.
As in the first leg against Warsaw, McGregor gave Celtic an early lead, stabbing home a loose ball after Jasmin Handanovic had parried Jo Inge Berget's initial effort.
McGregor's strike arrived in the sixth minute but Celtic's advantage was wiped out before the quarter-hour mark as Damjan Bohar slotted home.
Elsewhere in the play-offs, Zenit and Porto both claimed 1-0 wins, over Standard Liege and Lille respectively.
Andre Villas-Boas' Zenit took the initiative in their tie thanks to Oleg Shatov's 16th-minute goal, courtesy of an assist from Brazil international Hulk.
Porto, meanwhile, were grateful to Hector Herrera's winner just after the hour mark in France, which gave them a slender one-goal advantage to take into next week's return leg at Estadio Do Dragao.
In Denmark, AaB took a 16th-minute lead through Nikolaj Thomsen, only for Vinicius to hit back for APOEL to ensure the visitors return to Cyprus in the ascendancy.
Elsewhere, Slovan Bratislava needed a late Robert Vittek strike 10 minutes from time to earn a 1-1 draw at home to BATE, after Tomas Jablonsky had put through his own net in the 44th minute.