Alfredo Morelos scored twice as Rangers swept aside Midtjylland to set up a Europa League play-off round tie with Legia Warsaw.
Steven Gerrard's Scottish Premiership side were in a strong position after winning 4-2 in Denmark last week, but first-half goals by Morelos and Sheyi Ojo put the tie beyond doubt.
Morelos added his ninth of the term after the break, and although Evander pulled one back, Rangers will travel to Poland next week knowing they are 180 minutes from the group stages.
Gerrard's side are now just two games away from reaching the Europa League group stages in consecutive seasons after scoring 19 goals and conceding just three in just six qualifying games.
And under the Englishman, the Ibrox side have lost just two of 20 games in continental competition.
Free-scoring Rangers through in style
Gerrard was determined his side would not suffer the same European fate as city rivals Celtic earlier in the week. And, from the first kick, it was evident the Rangers squad had heeded his warning.
Midtjylland had travelled to Glasgow knowing they needed to score at least three goals and, while it was apparent from their efforts to get the ball up the park, it ultimately played in to Rangers' hands and allowed a front line of Scott Arfield, Ojo and Morelos to counter-attack with purpose.
It did not take long before the home side began to threaten. Ojo came close before swinging in a cross in from the left that allowed Morelos to pounce, cut inside Rasmus Nicolaisen, and knock the ball home.
Any pre-match jitters from the home crowd were quickly dispelled and, with the comfort of a three-goal cushion, Rangers struck again seven minutes from time. After a smart tackle from Ryan Jack in the middle of the park, Arfield then broke against a limited defence, before finding Morelos out wide.
The Colombian striker initially miscontrolled but managed to skid the ball to the front post where Ojo arrived to finish.
Gerrard's side began the second half with the same purpose as in the first. Ojo latched on to a thunderous clearing header from Nikola Katic just five minutes in to the half, then swung in a cross from the left that allowed Morelos to duly tapped in his second from just a few yards out.
If this Rangers side were capable of complacency then it understandably began to seep in after they had built up a five-goal lead.
The first hints of a Danish revival came in the 50th minute when Gustav Wikheim latched on to a long ball, skipped beyond James Tavernier and fired a tricky shot at Allan McGregor. Eight minutes later, the same forward forced another save from the Rangers goalkeeper after getting on to the end of an Awer Mabil cross.
The consolation would come 20 minutes from time when another Mabil cross found Evander in the box.
By then, Rangers had already turned their attention towards what was to come, although an injury to Morelos - who was forced to come off after his momentum took him crashing in to an advertising board - was one black mark on a bright evening.
- 11OjoSubstituted forJonesat 69'minutes
- 2TavernierBooked at 33mins
- 18KamaraBooked at 79mins
- 8JackSubstituted forDochertyat 69'minutes
- 20MorelosSubstituted forDefoeat 81'minutes
- 9KabaBooked at 76minsSubstituted forDovbykat 82'minutes
- 20NicolaisenBooked at 45mins
- 14ScholzBooked at 51mins
- 10da Silva Ferreira
- 34AndersonSubstituted forSparvat 69'minutes
- 38Ogochukwu Onyeka
- 40CajusteSubstituted forMabilat 45'minutesBooked at 65mins
- Marco Di Bello