Claudio Caniggia, with two goals, and Tore Andre Flo were the men who found the net and all three goals were excellent, but it was the wing play and the endeavour of McCann which caught the imagination of the fans.
He looked like a man who meant business in everything he did and Advocaat must be seriously considering promoting him to the staring line-up for this weekend’s game with Livingston.
It certainly was not all roses for Rangers, however, and watching Fenerbahce assistant boss Oguz Cetin must have been heartened by their slipshod start to the match.
Psychologically, Rangers may have thought the tie had been won in Slovenia and it showed in their early play which was one-paced at best.
There were a couple of decent moments when Bert Konterman hit a freekick just over in eight minutes after Christian Nerlinger had been brought down and then Caniggia fired just too high after linking well with Russell Latapy.
However, the apparent complacency manifested itself in the worst possible way when slackness from Konterman gifted a shock opening goal for Maribor in 17 minutes
The big Dutchman seemed to have everything under control when Simon Seslar played the ball through to the edge of the box but Konterman was too casual and allowed the ball to run under his left foot.
Vanja Starcevic could not believe his luck but did not waste any time taking advantage as he took possession burst forward and drove a right foot shot past a most unhappy Stefan Klos.
The Ibrox crowd was stunned and this was clearly not in manager Dick Advocaat’s plans. He immediately vacated his seat in the stand to take a more hands-on approach and little wonder.
Rangers were in trouble again three minutes later when they could not defend Bostjian Znuderi’s corner from the left, allowing Seslar a free header but the effort looped over.
Nerlinger tried to get Rangers going with a great interception and stinging volley which flew just wide in 22 minutes, but he hurt his left ankle in the process and this led to his withdrawal 16 minutes later.
It was another blow Advocaat could have done without but on the positive side rookie midfielder Stephen Hughes, making his first start for the club, nearly equalised in 25 minutes.
Flo was the creator, bursting into the box before laying the ball back to Hughes who tried to the lift a right foot shot into the net but keeper Marko Simeunovic produced a terrific save.
Rangers were not quite out of their lethargy, however, and it took some half-time words of encouragement from the manager to really get them going.
Two goals inside the first 12 minutes of the second half made the job secure and the equalising strike in particular was quite excellent.
Barry Ferguson was quiet by his standards but it was his accurate pass wide to Neil McCann, who had replaced Nerlinger, which initiated the move in 54 minutes.
McCann then showed all of his ability as he danced in from the left, linked brilliantly with Caniggia before sweeping a low cross to the back post where Flo slotted the ball into the net.
Any mild panic which had existed in the Stadium was gone and Rangers took the lead in 57 minutes. Again it was an excellent move with Caniggia starting and finishing it.
The 34-year-old Argentinian swept the ball wide to Fernando Ricksen who burst forward and released Hughes who had made an excellent diagonal, darting run.
Sadly for the teenager, the keeper blocked his shot at goal but the ball broke to Caniggia who had sensibly followed up and he scored with some ease.
Caniggia and Rangers were not finished, however, as they exemplified the difference in class between the two sides with a third goal in 73 minutes.
Again Ricksen was involved with a solid ball forward into the box, but it was Flo’s lay-off which made it. The Norwegian used the pace of the ball to play it into the path of Caniggia whose finish was lethal, as he slid a right foot shot low into the right corner.
There was even time for Advocaat to give Billy Dodds his first piece of match action of the season as the Scotland man came on for Caniggia, who had performed his job excellently
In the end it was all too comfortable but Rangers simply cannot afford to be so slack when they face Fenerbahce next week when the stakes are absolutely massive.
RANGERS: Klos; Ricksen, Moore, Konterman, Vidmar; Hughes, Ferguson, Latapy (Wilson 53), Nerglinger (McCann 38); Caniggia, Flo. Subs not used – Mols, Dodds, Kanchelskis, Christiansen, Miller.
Bookings:
NK MARIBOR: Simuenovic (Murko 78); Buksanovic, Balajic, Krizan; Starcevic, Znuderi, Duro, Seslar, Filekovic; Kvas (Golob 61). Subs not used – Dvorsak, Ihtijarevic, Pitamic, Plosnik, Sarkezi.
Bookings: Kvas (33)
Att: 50,045
Ref: Jorge Emanual Monteiro Coroado (Portugal).
Man of the match: Neil McCann.
Moment of the match: McCann’s movement on the left for the first goal.