With their rivals not in action this weekend - Celtic's Scottish Cup tie at Inverness was postponed - the Scottish champions were well aware of the importance of taking maximum points.
El-Hadji Diouf's opener was cancelled out by Jamie Hamill from the penalty spot but it was Tim Clancy who had the final say when he was unfortunate enough to net an own goal late on.
Rangers were handed a double boost ahead of the match after Nikica Jelavic and Sasa Papac were both passed fit after being sidelined with a hamstring injury and concussion respectively.
Kyle Lafferty and Kyle Hutton were both named among the substitutes, while regular first-choice goalkeeper Allan McGregor was back between the sticks, with Neil Alexander named on the bench following his surprise appearance in Thursday's goalless draw against PSV Eindhoven in the Europa League.
Kilmarnock were without suspended duo Frazer Wright and Alexei Eremenko, with Garry Hay and Mohamadou Sissoko both drafted into the side, the latter having served his own ban.
Rangers had the chance to take the lead when Steven Whittaker collected the ball 20 yards out, turned and unleashed a shot that fell just wide of Anssi Jaakkola's right-hand post.
But Kilmarnock had started brightly and they had a decent opportunity of their own when Hay provided the cross from the left only for Liam Kelly to hook well over the crossbar when he should at least have tested the goalkeeper.
At the other end, Diouf's corner found Kyle Bartley and his header from close range looked netbound until Sissoko was able to nod just over with a last-ditch clearance.
A free-kick from Steven Davis 25 yards out was then deflected into the path of Diouf but the on-loan Blackburn man fired wide of the target.
Rangers continued to push forward in search of the opener and Manuel Pascali almost unwittingly handed them the lead when he came close to forcing a Madjid Bougherra cross into the back of his own net.
The breakthrough came after 38 minutes when Diouf netted his first goal at Ibrox to hand Rangers the advantage.
Whittaker supplied the pass and Diouf took a touch before rifling a right-foot shot past the grasp of the Kilmarnock goalkeeper and into the bottom corner from 10 yards.
Rangers could have doubled their lead shortly after the restart when Jelavic snatched the ball from the feet of Sissoko and decided to have a crack at goal himself, instead of picking out another blue jersey in the box.
But Jaakkola did well to stand up to the angled drive and blocked well at his near post before the danger was cleared by his defence.
Kilmarnock were back on level terms after 60 minutes when referee Alan Muir ruled that Bougherra had fouled Clancy in the box and Hamill stepped up to blast the penalty high into the back of the net.
Jelavic then claimed he was tugged in the box by Hamill just moments later but there was no spot-kick award at the other end.
With time running out to find a winner, Rangers threw Lafferty and Vladimir Weiss into the action in place of Diouf and Richard Foster with 15 minutes to go.
There was a shout for handball against Hay from the Ibrox crowd but Rangers had to settle for a corner instead and failed to capitalise on the flag-kick when Jelavic nodded over.
Killie boss Mixu Paatelainen clearly felt they should have had another penalty when Rui Miguel went to ground under pressure from Bartley, judging by his furious reaction in the dug-out, but the referee opted not to point to the spot on this occasion.
Rangers were back in front with three minutes remaining when Weiss flighted a dangerous cross into the box and Clancy inadvertently bundled the ball into the back of his own net to hand the home side the points.