When Kris Boyd pulled one back for the visitors with 15 minutes to go, it led to a nerve-wracking finish for Rangers.
It had all looked so easy for the Ibrox side at half-time when they led through goals from Dado Prso and Nacho Novo, but their inability to finish off Kilmarnock nearly cost them dearly in the end.
Rangers thought they had made an early breakthrough when Alan Combe spilled a Gregory Vignal effort leaving Prso to shoot home, but the striker was judged offside. Prso again went close with a flashing header. Kilmarnock also had the ball in the net, but Boyd had fouled before heading home.
Boyd then won a corner for the visitors with a header from a Steven Naismith cross as Killie rallied. Combe produced a marvellous double save to deny Novo and Vignal at the end of a patient build-up by the home side.
Rangers made the breakthrough on the half-hour mark with a superb goal by Prso. The Croatian striker collected Barry Ferguson's pass before side-stepping Simon Ford and curling a tremendous shot into the top corner from 25 yards.
Ferguson then shot over before Alan Hutton was stretchered off after a wild tackle on Garry Hay. Afterwards it was learnt that the wing-back would be out for six months with a broken leg.
Kilmarnock gifted Rangers a second goal just before the interval when Ford overhit a back-pass and Novo rounded Combe before sliding the ball into the empty net.
Prso threatened shortly after the break, but Combe managed to turn his shot round for a corner.
Rangers went close to adding a third which would have finished off Kilmarnock's challenge. In a swift counter-attack, substitute Steven Thompson swept the ball out to Vignal, whose first-time cross was met beautifully by Thomas Buffel only for the Belgian to see his shot come back off the base of the post.
Kilmarnock were back in the game when Boyd hooked his shot high into the net from Peter Leven's corner.
Combe kept his side in the match with a brilliant save from a volley by Sotirios Kyrgiakos, but Killie were not able to force an equaliser.