Kenny Shiels' side started with a five-man defence
and played with poise and purpose in the opening
half hour.
James Fowler delivered an excellent cross for Paul Heffernan, who just failed to connect with the header in front of goal, while a Gary Fisher thunderbolt from 30 yards fizzed narrowly wide.
Jelavic then slipped a pass through for Papac, who only had Bell to beat, but the keeper made a fine block from the point-blank effort.
Rangers upped the tempo in the final 15 minutes of the first half; Bell turning a Juanma Ortiz ball past the near post, with Jelavic loitering, and Edu shooting over.
The home side made a strong start to the second period and Bell threw himself in front of a Lafferty shot after the striker latched on to Steven Whittaker's headed knockdown.
The opening goal came from a well rehearsed free kick, Jelavic peeling away from the home defence to find the net with a deft sidefoot touch from near the penalty spot.
Kilmarnock came
close to an immediate equaliser when Rangers keeper
Allan McGregor flapped at a corner and Harkins hit
the crossbar with a header.
Having survived that scare, Rangers raced up the park and doubled their lead when Wylde played a one-two with Edu before rifling into the back of the gaping net from six yards.
Rangers should have had the net bulging again when Jelavic turned provider for Davis but Bell just managed to palm a dinked effort to safety.
Liam Kelly let rip from 25 yards and McGregor was relieved to see the ball fly narrowly wide, while Lee Wallace made a great tackle to deny Heffernan a one-on-one with the Rangers keeper.
From another Davis delivery, Jelavic shrugged off Zdenek Kroca with ease, only to blast over but Rangers had no cause for regreat as they held on comfortably for the win
Sandy's Match Pic's are HERE
