Alan Combe took a knock in training allowing Graham Smith to take his place in goal, but the 22-year-old had no chance with Rangers' opener in the 16th minute.
Simon Ford and Gordon Greer failed to clear Alan Hutton's routine cross and the ball fell invitingly for Shota Arveladze who drilled his 12-yard shot beyond the keeper.
The goal settled Rangers and they enjoyed a huge amount of possession without threatening Smith in the Kilmarnock goal. Killie soaked up the pressure and could have found an equaliser on a rare break forward.
Steven Naismith won the ball in his own half and found Kris Boyd who in turn set up Danny Invincibile and he was clean through with only Stefan Klos to beat.
Invincibile set himself to shoot from 20 yards when he had Colin Nish in acres of space on the right of the area, and his tame effort was collected simply by the keeper.
Both sides passed up chances to score in the closing minutes of the first half.
First Rangers broke forward through Arveladze who showed the awareness that Invincibile had not as he weighted a perfect pass for the onrushing Fernando Ricksen. His shot beat Smith but Freddy Dindeleux was on hand to hack the ball clear.
Arveladze had another chance in the 43rd minute after Gregory Vignal's probing pass had sent him clear but an uncharacteristically bad touch gave Smith the chance to slide out and smother.
Boyd's touch had been clumsy all day and he passed up a golden chance on the stroke of half-time. Naismith showed great composure to pick Boyd out in front of goal, but the striker missed his kick completely from point-blank range.
The second half was as scrappy as the first, but Dado Prso almost put the match beyond Kilmarnock six minutes after the break.
Rangers broke swiftly from a Killie corner and Smith threw himself to his right to finger-tip Prso's shot past the post. Alex Rae fired a great shot inches wide a minute later, and the home goal led a charmed life in the 62nd minute.
Smith pulled off another great save to deny Ricksen, and Hamed Namouchi looked certain to score when the ball was chipped back in from the rebound, but Simon Ford got back to head the ball off the line.
Boyd had another chance to square the match in the 73rd minute. Invincibile caught Vignal napping and stabbed the ball to the striker.
He cut inside the last defender but found Klos in the perfect position to save.
Kilmarnock enjoyed their best spell of pressure in the closing minutes as they tried to rescue a point, but it was too little too late.