Sparta had been the only side to stop Rangers winning under Clement in the reverse fixture, but there were worrying signs early on for the Czech outfit.
Sam Lammers slotted Todd Cantwell in early, but the Englishman was caught in two minds between crossing and shooting, with the ball eventually trickling wide.
His indecision wouldn’t prove costly, as moments later James Gomez’s terrible backpass was intercepted by Danilo, who had the simple task of slotting home the opener.
The famous Ibrox crowd was well and truly behind their team, and by the 20th minute, the Gers had doubled their advantage.
Danilo turned provider, slotting in Cantwell, who cut inside Gomez before applying an almost identical finish to the opener for his first goal of the season.
Sparta were woeful, and errors from Asger Sørensen and Gomez almost saw them fall further behind, but Danilo struck the post and Cantwell was denied by a stellar save from Peter Vindahl before the break.
A double change at the break saw Sparta emerge greatly improved for the second period, but it was the introduction of Lukáš Haraslin that really saw the visitors begin to threaten. First, he saw a diving header drift just wide of the post before he volleyed into the ground and narrowly wide of Jack Butland’s upright.
Those scares appeared to spark Rangers back into life, and it was soon their turn to threaten through Ross McCausland and Ryan Jack, although both were eventually denied by Vindahl. Sparta’s pressure would eventually tell, however, as Haraslin brilliantly rifled home from Angelo Preciado’s cutback to reduce the arrears.
The Slovakian was a constant source of problems for Rangers, and his mazy run earned him a shot at an equaliser that was brilliantly denied by Butland.
Far from the cauldron it had been earlier in the night, Ibrox was now a nervous wreck as the hosts desperately held on to their slender one-goal lead.
Eight added minutes weren’t helping that cause, but the Scottish giants managed the closing stages superbly as Sparta’s winless run in away European games extended to 11 matches as their UEL campaign hangs in the balance.
Flashscore Man of the Match: Danilo (Rangers)
