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.
5. Connor Goldson - 6
In the spotlight and steady enough performance at heart of defence, but caught ball-watching at McGregor's late double-save. Photo: Andrew Milligan
6. Glen Kamara - 8
Drew foul after foul in the middle of the park playing it simple and holding possession in pressure areas. Consistently reliable, yet showed a different side to his game under his new manager in the slightly different midfield role. Adaptable. Photo: Alan Harvey - SNS Group
7. Steven Davis - 7
European ever-present this season kept it ticking and had an extra spring in his step linking the free-flowing passages in the first half in the double-pivot, then kept it neat and tidy after the interval. Photo: Alan Harvey - SNS Group
8. Joe Aribo - 7
Should be rated so much higher but profligate in front of goal. Could have had a hat-trick and in all the right positions but just no end product. Hit the bar biut also wasted a great chance over it in the first half. Photo: Andrew Milligan