The home team went ahead early on through Jean-Claude Darcheville and when Steven Whittaker added a second ten minutes after the interval there was no way back for the visitors.
Rangers' victory would probably have been even more emphatic if referee Alan Freeland, who had a poor match, had not turned down two or three strong penalty claims by the home side.
Rangers made a whirlwind start with Grant Murray just managing to clear from Darcheville with keeper Alan Combe stranded. Then Lee McCulloch headed Barry Ferguson's corner just wide before the home side took the lead.
McCulloch's header to Kris Boyd was cleverly flicked on by the striker to Darcheville, who outpaced Ryan O'Leary before sliding his shot into the corner of the net.
Rangers nearly added to their lead when Boyd's pass found Steven Naismith, but he pulled his shot wide from a good position.
Darcheville limped off after half an hour to be replaced by Charlie Adam, but it was Killie who squandered the chance to equalise just before half-time. Kevin Thomson lost possession to Mehdi Taouil and his pass released substitute Colin Nish, but the striker failed to take advantage and shot tamely wide.
The home team went further ahead just after the break with a well-taken goal. Naismith, who came on to a good game in the second half, sent in a reverse pass which Whittaker gathered before stepping inside Simon Ford and unleashing a powerful shot into the top corner of the net.
Naismith fired narrowly wide before Boyd did have the ball in the net after Combe fumbled Adam's shot, but the striker was ruled marginally offside.
Referee Freeland turned down two strong penalty claims from McCulloch and Adam much to the annoyance of the home support, but in the end Rangers were happy to see out time.