The hosts were in control for much of the opening stages but initially failed to take the initiative, with Cerny and Igamane combing well on several occasions and the latter twice firing narrowly wide.
John Souttar flicked over from close range before Ianis Hagi’s cross found Tavernier, who drifted in at the back post and lifted the ball over Robby McCrorie.
Igamane and Danilo both had efforts saved well by McCrorie as Killie struggled to get up the pitch before the interval.
A quickfire double at the start of the second half killed off any hope the visitors had of upsetting Clement's side again this term. Danilo turned in Hagi's low cross and Igamane capitalised on a poor Corrie Nbada clearance with a thumping strike.
One of Rangers' most potent attacking outlets this season, Czech international Cerny scored the fourth with a reversed finish into the bottom corner after Nicolas Raskin dribbled into the area and nudged it to the winger.
Dessers, the Ibrox side's top scorer this term, saw his first goal initially ruled out for offside after he tapped in Jefte's flashed cross, but it was awarded following a VAR review.
The striker, on as a second-half substitute, added his 12th of the season with a composed first-time finish from Tavernier's whipped ball.