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.
9. Ryan Kent - 7
Played in a wider role and brought a new element, still a constant threat and should have had a goal of his own - or an assist for Morelos' hat-trick in the second half. A changed man from his Hampden outing on Sunday. Photo: Scott Heppell
10. Ianis Hagi - 7
Substituted after 70 minutes but gave a lot in his appearance. Brave to lay on Morelos' opener and technical ability looks tailor-made for van Bronckhorst's style. Visibly enjoyed his role in the victory. Photo: VIRGINIE LEFOUR
11. Alfredo Morelos - 9
Point proven? Nearly. Played with a smile and delivered a mature performance after a horror-show at Hampden. Two goals, well-taken, and perhaps should have had a third laid on by Kent. Staked a claim under his new boss and tracked back when necessary while being in the right place at the right time. Photo: Ian MacNicol