The visitors did a fine job of stifling Rangers for a little over an hour before Steven Davis’ well worked free kick gave Jelavic to rifle home left footed.
Killie were almost level within minutes when Gary Harkins crashed a header against the bar but Rangers broke immediately and Mo Edu’s strength set up a tap-in for Wylde.
Edu had been by far Rangers’ most impressive performer until the first goal on a night where it looked like they might be left frustrated.
McCoist’s side were shorn of the energy of Steven Naismith after the midfielder was handed a two match ban and his absence was keenly felt in the opening 45 minutes.
In contrast to their victory at East End Park the Light Blues struggled to get the tempo up in the early stages of the game.
There would be no early scoring this time for the Light Blues and they were mere inches away from going behind after nine minutes.
Dorin Goian missed a ball swung in from wide on the Killie right and Paul Heffernan was so close to nodding it past a helpless Allan McGregor.
Rangers did clear and from the resulting corner Gary Fisher fired a decent long range effort just beyond McGregor’s upright.
Maurice EduStill that failed to spark the home side in to life and when Sasa Papac went down in the centre circle it looked like McCoist might be forced in to a change.
However the Bosnian continued after some attention from physio Pip Yeates and it was the left back that had the home side’s best chance so far on 21 minutes.
He continued a forward run and collected a neat pass from Jelavic but was denied when his low shot was well blocked by Cammy Bell.
With McCoist on the touchline urging his side to play higher up the pitch the home team did create more opportunities without ever really opening up the visitors.
A moment of brilliance from Jelavic almost saw him work Bell but his control from a ricochet and quick shot was just wide and high.
The home side were enjoying the better of the aerial contests with Carlos Bocanegra and Jelavic winning the majority of corner’s and crosses.
With six minutes of the half remaining, the crowd in the Copland Road stand were screaming for a penalty when Jelavic won a header but was caught by Manuel Pascali.
The appeals from the bench were more vociferous than Jelavic’s own, though the Croatian clearly felt he had been barged.
He almost earned his rewards in the final minute of the half when he met another Steven Davis corner and powered a header in to the ground.
Dorin GoianIt was almost identical to his Old Firm equaliser a little over a week earlier but this time it bounced a little too high and ended up over the bar rather than in the net.
The first 15 minutes of the second period ran largely along the same lines as the opening half until Lafferty had the chance to work Bell on the hour mark.
Edu’s deflected shot was nodded on by Steven Whittaker and Lafferty smashed his effort goalward only to see Bell throw himself in front of it to block.
The keeper needed treatment but the delay didn’t affect the home side and they were in front three minutes later.
With a free kick awarded wide on the left, Killie packed their box again but Davis’ low delivery found Jelavic in space and he made now mistake with his left foot drive.
That looked to be the visitors’ resistance broken but Harkins’ header at the other end off the bar was a warning.
And it was one that was heeded in the best possible style as Rangers responded with a brilliant counter attacking goal.
The superb Edu exchanged passes with Wylde and muscled his way in to the visitors’ box where the ball broke in to Wylde’s path to give the midfielder the easiest of finishes.
That opened the game up and Rangers might have added to the scoring when Davis broke free with a little over ten minutes remaining only to see his deft chip well saved.