Steven Gerrard's men have started the new season in impressive fashion, following up a 4-2 first-leg defeat of Midtjylland by putting six past Hibernian in the Scottish Premiership.
Rangers were comfortable again in a clinical display as Alfredo Morelos, taking his tally to nine for the campaign with a brace, and Sheyi Ojo each found the net.
Gerrard had the luxury of leaving Jermain Defoe, the weekend's hat-trick hero, on the bench until the 81st minute, and Legia Warsaw now lies between Rangers and the competition's group stage.
The host dictated play from the outset and lovely movement from Ojo allowed him to centre to Morelos for the opener, the striker shimmying away from Rasmus Nicolaisen in the area and finishing from close range.
Jesper Hansen made a smart stop to deny Morelos his and Rangers' second with a drive from a tight angle, while Midtjylland was wasteful at the other end despite promising forays of its own.
The visitor was duly punished as Morelos turned provider for Ojo to sweep home a low cross, with only an excellent Hansen save keeping the same man from making it 3-0 with a free-kick before the break.
Rangers' front two continued to combine and it took just four minutes of the second period for Ojo to again pick out Morelos, who slammed home at the near post.
An outstanding Allan McGregor stop denied Gustav Wikheim when he looked destined to pull a goal back, before Evander did belatedly get Midtjylland on the scoresheet with a first-time finish.
But the visitor's best efforts proved far too little, far too late and Sory Kaba was slightly fortunate to escape with a yellow when he lunged in on McGregor late on.