It was left to Rod Wallace, the man who has taken over from Rangers' record goalscorer, to prove the difference with a 10th-minute strike, to which more should have been added.
With so much at stake, it was no surprise that the opening exchanges were frenetic. Kilmarnock, though, had little to fear, as they had won on their last visit to Ibrox seven months ago, and they should have taken the lead after five minutes.
Giovanni Van Bronckhorst's error allowed a long ball from Kevin McGowne to drop right in the path of Jerome Vareille. The Kilmarnock striker raced in on Antti Niemi but wasted the chance by shooting straight at the Rangers goalkeeper.
The folly of that miss was almost underlined as Stephane Guivarc'h volleyed a wonderful shot into the roof of the net a couple of minutes later but, fortunately for the visitors, the French striker was ruled offside.
However, there was no reprieve when Rod Wallace scored in the 10th minute. Barry Ferguson provided the perfect cross and the former Leeds striker stole in behind Kilmarnock's defence to stab his shot past Gordon Marshall.
Kilmarnock, at once robbed of their confidence and purpose, then had to soak up constant pressure. Losing Vareille to a dislocated shoulder did not help. However, had Guivarc'h found the target in the 21st minute, Bobby Williamson's side would have been finished.
Kilmarnock discovered their appetite in the second half with a far more effective pressing game, but chances remained the prerogative of Rangers.
Lorenzo Amoruso shamefully headed wide Van Bronckhorst's delightful free- kick, and Marshall produced a fine save on 57 minutes to deny Jorg Albertz from finishing off Andrei Kanchelskis' teasing cross.
Ibrox's frustration was evident at scant reward for such pressure and Van Bronckhorst was yellow-carded for a snapping foul on Gus MacPherson. Those nerves were not soothed as McCoist, the predator who rescued Rangers so often before his summer transfer, came on in the 74th minute for Paul Wright. But within minutes, Marshall had denied Rangers' substitute, Ian Ferguson, twice.Reuse content