The Czech side can’t catch the Scottish champions now after the two-goal victory and they enter the last 32 after an exciting evening in Ibrox.
Under Steven Gerrard they lost the first goal 12 times in the early part of the season – but new manager Giovanni van Bronckhorst turned that particularly unwanted statistic on its head as Alfredo Morelos swept the home side ahead with a first-time finish to round off an incisive passing move after patient build-up.
At times the ball flowed freely side to side and Rangers, in a 4-2-3-1 set-up looked to hurt Sparta more. Joe Aribo, who had already hit the post, spurned another chance and the home side went in a goal up, despite some gentle pressure from the visitors as the first period wore on. Allan McGregor had to be sharp to clear an overhit backpass and divert a close-range effort around his post too.
The goalkeeper was called upon with an incredible double save late on which kept Rangers ahead, head-to-head against Sparta after Morelos' second - a gift from some panicking defending from the Czech side.
Giovanni van Bronckhorst will be delighted with his first result, and his first team selection - here's how they rated.
Player ratings scale - 10: One of best performances you've seen. 9: Outstanding. 8: Very good. 7: Good. 6: Average. 5: Poor, 4: Very poor. 3: Terrible day at office. 2: Abysmal. 1: One of worst performances you've seen.
![Sharp to prod a close-range effort round the post in the first half's closing stages and dealt with an overhit backpass by Tavernier, but European specialist leapt into action with an incredible double save late on that ultimately confirmed Rangers were through.](https://www.thestar.co.uk/webimg/b25lY21zOjdkNTNjYmM5LWE2NmQtNDE5YS1iZTExLTU2ODgxYTQyMWRlODpiYzcyM2M1NC0xZjY2LTRhZWUtYTAyOC05MDNmZmNlMjVmOGY=.jpg?crop=3:2&width=640)
1. Allan McGregor - 9
Sharp to prod a close-range effort round the post in the first half's closing stages and dealt with an overhit backpass by Tavernier, but European specialist leapt into action with an incredible double save late on that ultimately confirmed Rangers were through. Photo: Rob Casey - SNS Group
![Captain was tidy enough but gave McGregor a scare with an over-weighted backpass in the first half. Less an attacking threat than usual and tucked inside further once Patterson came on.](https://www.thestar.co.uk/webimg/b25lY21zOjkxM2U4ODIxLTBiODktNGQ2Ny05OGNmLWIyODg1YTkwMWM5ZTozMmIyNzU4Mi04NGViLTQyYTgtODU5MC1iMTc0YmNmMDU0YWY=.jpg?crop=3:2&width=640)
2. James Tavernier - 6
Captain was tidy enough but gave McGregor a scare with an over-weighted backpass in the first half. Less an attacking threat than usual and tucked inside further once Patterson came on. Photo: Scott Heppell
![One of many looking refreshed and hit the by-line frequently in the first half but picked up a cheap and clumsy yellow card.](https://www.thestar.co.uk/webimg/b25lY21zOjk3NjljYzUzLTc2ZDItNDZkMy1hYzc3LThkYWY2ZjMxMzQ0YTo1ZmVkMGU4NS01Mzc2LTRhYzUtYmU4Yi03NDJhOTAwNDFhNGM=.jpg?crop=3:2&width=640)
3. Borna Barisic - 7
One of many looking refreshed and hit the by-line frequently in the first half but picked up a cheap and clumsy yellow card. Photo: Andrew Milligan
![Terrific start to finish. Positioned well, brave, quick and strong Bassey also gave an attacking threat but his defensive work was sound and may well have displaced Balogun in his less usual central position.](https://www.thestar.co.uk/webimg/b25lY21zOjE0YTQ0OTQ2LWFiNjMtNGE3NC1iNzgyLTllYzRiNWIzZDIzMTpiODBhZmQyZC1mNjE3LTQxOTUtOGIyZi1jMmFmYmMzZmQ1ZjA=.jpg?crop=3:2&width=640)
4. Calvin Bassey - 8
Terrific start to finish. Positioned well, brave, quick and strong Bassey also gave an attacking threat but his defensive work was sound and may well have displaced Balogun in his less usual central position. Photo: Andrew Milligan