Goals either side of half-time from Alfredo Morelos gave Giovanni van Bronckhorst's side a 2-0 triumph.
Rangers' day was made even more sweeter given fierce rivals Celtic exited the competition.
Celtic needed to pick up at least a point against Bayer Leverkusen to have any chance of progressing through group G.
It looked as if they would get what they desired as they held a 2-1 lead with 10 minutes remaining in Germany.
But goals from Robert Andrich and Moussa Diaby saw them succumb to a 3-2 defeat and crash out of the competition.
Kris Boyd, who scored 138 goals for Rangers across two spells, was covering their game against Sparta Prague on Sky Sports.
And he couldn't help trolling Celtic after the two sides' mixed fortunes on the evening.
"Just on that, I believe, I've heard there have been a few Celtic fans wondering where I've been the last few days.
"They won't need to worry, I'll definitely be here speaking about Rangers in the knockout stages of the Europa League.
"And, as we know after tonight, that's not for everyone!"
Sancho SCREAMER seals it! Full reaction to Villarreal 0-2 Man Utd on The Football Terrace...
Boyd put his thumbs up to the camera and let out a beaming smile as he delivered the final line.
Unsurprisingly, Rangers fans have thoroughly enjoyed Boyd's comment, with one video picking up over 4.5k retweets at the time of writing.
Both sides still have one game remaining in the group stages of the Europa League.
Rangers travel to Lyon on December 9, while Celtic host Real Betis on the same day.
Both games are dead rubbers as Rangers and Celtic are assured of finishing second and third in their respective groups.