Ally McCoist included midweek goalscorer Thomas Bendiksen from the start as he made three changes to the side that lost at Rugby Park six days earlier.
Lee McCulloch, Kyle Lafferty and Ross Perry all dropped out with Bendiksen, Kyle Bartley and Gregg Wylde taking their places.
Rangers started more brightly than they have done in many weeks with Aluko instantly doing his cause with the home fans no harm with a darting run down the right to open things up in the opening minute.
Bendiksen had also started in a mood to impress and he contributed to a really positive opening spell from the home side.
It took until the ninth minute for the first real chance to appear when Davis’s floated delivery found Jelavic in the box, but the Croatian headed wide.
Aluko then fed the striker a minute later in the right channel but the visitors’ defence managed to crowd out him and Whittaker following up.
It was recent signing Aluko who was looking most threatening, but with Wylde wide on the left as well and Bendiksen probing too, the home side were well on top.
After Aluko shot over 15 minutes in he almost found the net when he followed in on a well saved Wylde shot from the edge of the area.
The pressure was beginning to tell and after Aluko had a penalty claim turned down on 19 minutes the breakthrough came on 21 minutes.
It was a neat exchange between Whittaker and Bendiksen on the edge of the area before the Norwegian midfielder pressurised the visitors in to a mistake and Paul Gallacher’s attempted clearance came back off his own defender and looped in.
It was the goal that the home side’s domination deserved and they extended their lead seven minutes later when Aluko did win a penalty.
Jelavic made no mistake from the spot and from there it looked like the home side were in for a comfortable afternoon.
But within three minutes they were pegged back when Joe Cardle broke down the left and cut in past Dorin Goian to fire low beyond Allan McGregor.
It was the Pars first real chance in a half dominated by the home side, and Rangers almost restored the two goal advantage instantly.
Davis and Jelavic exchanged passes but the Ulsterman’s low drive was well blocked. He then nearly turned provider when he nodded in to the path of Wylde who saw his right foot effort drift wide.
Again at the start of the second period it was the home side that started more brightly, with Bartley seeing an effort blocked for a corner three minutes in.
Aluko then again threatened on the right as he danced his way in to the box only to see his shot across the face of goal well defended.
Bendiksen was withdrawn just before the hour mark with Lafferty introduced, and that meant a change of shape for the home side.
It also seemed to cause a break in momentum as chances became fewer and further between, Jelavic enjoying the better opportunities, but being denied twice by Gallacher.