After a few early scares Charlie Adam settled the home team's nerves with a well-struck shot. Kris Boyd scored a second soon after and when Dado Prso netted just before the hour mark it was all over for the visitors.
Kilmarnock went close early on when Danny Invincibile outjumped Sasa Papac at the back post but his header drifted narrowly wide.
Rangers responded well when Alan Hutton cut the ball back to Boyd and when the striker's shot was blocked, Nacho Novo crossed to the far post where Prso produced a superb overhead shot which keeper Graeme Smith parried away.
The home side's opening goal was not long delayed. Prso crossfield pass found Adam, who advanced on a retreating Killie defence before rifling a right-foot shot into the top right-hand corner.
Rangers added a second when Smith did well to touch away a cross from Novo, but the ball fell to Boyd, who bundled the ball home from close range.
Karl Svensson did well to intercept a Gary Wales cross as Invincibile was poised to shoot.
Rangers nearly added a third just after the break. Novo's volley struck substitute Simon Ford, but Smith reacted well to push the ball away.
Svensson looks to be growing in confidence and again intercepted a dangerous Garry Hay cross before Rangers made the point safe.
A superb pass by Boyd across the 18-yard line reached Prso, who stepped inside Fraser Wright before shooting home at the near post.
This was the last involvement of the Croatian, who went off to much applause.
Rangers would have added more if it had not been for some heroic late saves by Smith, especially from substitute Thomas Buffel.