A David Weir header calmed the visitors' nerves before Kris Boyd shrugged off a nightmare 45 minutes to score his customary goal at Rugby Park before Kenny Miller and Steven Whittaker added two more late on.
Killie's central defensive injury jinx struck again as David Lilley was added to the unavailable list pre-match because of a stomach problem. This meant that Fraser Wright was rushed into action earlier than anticipated to add some stature to a diminutive rearguard.
Rangers kept faith with the starting eleven that had shared six goals with Dundee United.
Killie's lack of physique was evident in the fifth minute when Kevin Thomson swung in a free-kick which Madjid Bougherra almost bundled home.
The expected Rangers onslaught failed to materialise and it was an even contest for the first half-hour.
The Ibrox side were handed a golden opportunity to take the lead when they were awarded a soft penalty when former Killie hero Boyd tumbled in the box when backing into James Fowler.
The striker took the spot-kick himself, but Alan Combe stayed strong and deflected the blasted effort over the bar with his legs.
Rangers' frustration increased as they rattled the woodwork twice in three minutes. Boyd's magnificent 35-yard effort flew back off the face off the crossbar and then Nacho Novo saw his right-foot effort strike the base of the post.
Boyd then missed another gilt-edged chance five minutes before the break when the home defence messed up their offside trap leaving him alone in the box.
He took the ball past Combe, but the keeper somehow managed to recover and put Boyd off, and the defence managed to regroup and clear the danger.
Rangers came out fired up after the break. Wright made a brilliant tackle to deny Miller, but Killie's set-piece weakness cost them in the 50th minute. Thomson swung in a deep corner and captain David Weir headed home unchallenged from close range.
The Gers doubled their lead four minutes later with a clinical breakaway goal. Killie lost possession on the edge of the Rangers box and the ball was played wide to Miller.
He played a great cross-field ball to Boyd who, despite his previous misses, coolly beat Combe from the edge of the box.
Both sides were hit by injuries as Killie's Jamie Hamill and Rangers' Thomson were stretchered off in separate incidents.
Rangers added a third goal from another set-piece three minutes from time when Miller headed home Steven Davis' deep cross and made it 4-0 in stoppage time when substitute Whittaker reacted well to a deflected Davis cross before deftly lobbing the ball over the helpless keeper.