Two goals from Tore Andre Flo and a debut strike from Christian Nerlinger earned Rangers an emphatic victory in Maribor.
Now it remains a formality for Dick Advocaat's side to complete the tie at Ibrox next week and move on to the final Champions League qualifier with Turkish champions Fenerbahce.
That will inevitably be far tougher, but Rangers had little option beforehand to regard Maribor as the most daunting of opponents at this stage of the competition, and until Flo's opener the story of the first half was confirmation of that fear.
The goals that were to come made this a comfortable victory, but until then it was anything but.
The Slovenian champions' pass and move methods often stretched the Rangers back four, which had seen Bert Konterman moved up into midfield.
Claudio Caniggia was one of three summer signing debutants, alongside Russell Latapy and Nerlinger, and he and Flo were both turning up in the Maribor box more regularly by the half-hour mark.
Flo initially had been admirably shackled by Ales Krizan, the left-sided defender who had been part of Barnsley's Premiership season in 1997-98.
But when Latapy, who had been teed up by a sublime Caniggia pass, lofted the ball into the penalty area it was just where the Norseman likes it - in his path and on the ground. His finish was top-drawer; across Simeunovic and into a bottom corner.
Advocaat made a change at the break, bringing on skipper Barry Ferguson, and it did not take long for Ferguson to make an impact and he almost sent Caniggia clear.
And when he did find the Argentinian on the edge of the area it led to the second goal, in the 56th minute.
Caniggia crossed to the far post where Flo was lurking and his nod back was perfect for Nerlinger to drill home off a post.
Michael Mols came on for Caniggia with 20 minutes to go and was almost on the end of an enticing cross by Fernando Ricksen to the near post.
Mols could not quite connect and the ball continued on its way into the danger area where Flo and Balajic collided. Flo converted the penalty.
Nk Maribor: Simeunovic, Duro, Krizan, Seslar (Golob 58), Dvorsak, Sztipanovics, Filekovic, Balajic (Znurderl 88), Sarkezi, Cipot (Kvas 73), Snofl. Subs Not Used: Murko, Pitamic, Starcevic, Vuksanovic. Booked: Sarkezi.
Rangers: Klos, Moore, Amoruso (Ferguson 46), Numan, Konterman, Nerlinger (McCann 64), Ricksen, Reyna, Caniggia (Mols 69), Flo, Latapy. Subs Not Used: Christiansen, Miller, Johnston, Vidmar. Booked: Amoruso.
Referee: M Van Der Ende (Hol).