Tore Andre Flo bagged a first-half double to take Rangers a step closer to a place in next season's Champions League.
But it was a night to forget for Ibrox legend Ally McCoist, who in probably his last game against his former club before hanging up his boots, missed the chance to score for Kilmarnock from the penalty spot.
After his team's dreadful injury problems this season, Rangers manager Dick Advocaat was able to select a rare unchanged side from the one which drew with Hibernian at Easter Road on Sunday.
Kilmarnock were also hoping for a European place and manager Bobby Williamson named the same side which beat Dunfermline at the weekend.
But the visitors drew first blood after just 45 seconds with the opener from Tore Andre Flo.
Claudio Reyna found Barry Ferguson in space and he played the ball to the Norwegian, who evaded a poor challenge from Chris Innes before drilling low into the bottom corner from a tight angle.
Rangers were clearly fired up to put on a show for their big travelling support and in the fourth minute Rod Wallace fired just past the post from the edge of the area.
The home defence were living dangerously and almost fell further behind in the 11th minute when Billy Dodds controlled Reyna's long ball before dragging his effort just wide.
But Kilmarnock were gifted the opportunity to draw level in the 14th minute when referee Eric Martindale controversially pointed to the spot when Kevin McGowne went down in the box.
Justice was done, however, moments later when Ally McCoist, in possibly his last game against his former club before he retires, stepped up.
Rangers goalkeeper Stefan Klos pushed the Ibrox legend's effort on to the post and he even got up to make another great stop to deny Andy McLaren's follow-up shot.
Rangers skipper Ferguson was booked for dissent after the penalty decision and Scott Wilson followed him into the book for a clumsy challenge on McLaren.
The referee was upsetting both sets of supporters and in the 27th minute booked Antonio Calderon for an innocuous foul on Wallace in the centre circle.
Rangers continued to play plenty of nice football as the home defence looked to hang on.
Meldrum had to touch behind Reyna's dangerous corner kick, but in the dying seconds of the half Rangers deservedly doubled their lead.
Fernando Ricksen crossed from the right wing for Flo to tap home from close range for his second of the night.