Gers weren’t to be denied though and substitute Vladimir Weiss forced Tim Clancy into scoring past his own keeper in a pulsating closing sequence.
The narrow 2-1 win moves Walter Smith’s men to within two points of Old Firm rivals Celtic at the top of the league table.
And with another extra game to play, the champions’ destiny is still very much in their own hands with 11 matches to go.
Now Rangers will prepare for huge games against PSV Eindhoven in the Europa League and Celtic in the League Cup final this week.
This match might not been the most easy on the eye but the battling manner of the win will give the team a big boost going into the next few days.
With key players available again following injuries, it wasn’t a great surprise to see Smith shuffle his pack ahead of those meetings with PSV and Celtic.
Nikica Jelavic and Sasa Papac both returned to the first XI, while Allan McGregor was back in goals again after warming the bench in Eindhoven.
That meant Kyle Hutton, Kyle Lafferty and Neil Alexander all dropped out, with each of the trio taking a place on the bench.
Rangers made a bright start and forced their first attempt on goal inside 60 seconds but Steven Whittaker’s deflected effort just eluded Maurice Edu six yards out.
The former Hibs full-back then came close to creating a chance for Jelavic after winning a strong tackle and playing a neat one-two with Diouf.
But despite a decent enough delivery into the box, Whittaker’s Croatian team-mate was crowded out and Killie cleared the danger.
That almost proved costly when the visitors almost went in front with their first meaningful foray upfield.
Gers failed to clear a corner from the right and David Silva, a scorer in his side’s win at Hearts last weekend, had time to curl towards goal.
He was unfortunate to see his effort bend past the post but the opportunity gave Kilmarnock confidence and they were showing they’d be tough opponents to see off.
The Ayrshiremen were packing their midfield and as such were proving difficult for the hosts to break down.
That meant they resorted to trying their luck from distance and the busy Whittaker wasn’t far from hitting the mark with a good drive from 25 yards.
At the other end, Hamill – a scorer at Ibrox on the opening day of the season – had a chance to grab another goal but was woefully wasteful and fired well over.
There were plenty of openings in the opening exchanges and Kyle Bartley almost broke the deadlock from a Diouf corner.
But just when it seemed the on-loan Arsenal defender’s header was bouncing back up off the ground and in, Mohamadou Sissoko got a crucial touch to help it over the bar.
Diouf had a glorious opportunity to net when a Steven Davis free kick spun off the wall and into his path.
But the ex-Senegal international somehow contrived to put the ball past the post from close range when it seemed easier to force it home.
The Light Blues simply weren’t getting the breaks they desired and Madjid Bougherra’s teasing low cross into the mix looked set to roll in when Manuel Pascali connected.
He was let off the hook though when his keeper Anssi Jaakola saved him from scoring an embarrassing own goal as he stopped it on the line, albeit without knowing much about it.
Frustration was setting in amongst a home support which was eager to see Rangers make the most of their chance to close the gap at the top of the SPL.
And when Bougherra charged forward and sent in a cross which was far too deep for any of his team-mates to reach, the sighs around the ground summed up the mood.
Bartley has shown himself to be a real threat at set pieces, with his first senior goal at St Mirren nearly followed by a second in Holland.
And having gone close earlier in the game, he again beat Jaakkola to an outswinging Diouf corner but his header flew inches over.
Jelavic was blocked too after a smart free kick from Davis following a foul on Richard Foster by Clancy.
It seemed only a matter of time before a goal would come and with Gers piling on pressure shortly before half-time, they went in front seven minutes prior to the interval.
Killie lost the ball in the middle of the park and Whittaker took over, taking time to assess his options before passing to Diouf in the right channel.
He took a touch to control then picked his spot before stroking in his first goal at Ibrox and his first in a league match for almost a year.
Going ahead did much to lift spirits around the stadium and having been happy to sit in and absorb previously, the onus was now on Kilmarnock to attack.
But Rangers had their tails up and although they missed further chances to strike before the break, they merited their 1-0 lead at the midway point.
There was a quieter start to the second half but Jelavic almost brought the game to life again when he took the ball from Sissoko.
He then cut inside and beat his man with quick feet but while his effort was on target, Jaakkola held it comfortably.
While they only led 1-0, the home side were treading a very thin line and as Killie gradually came into the game more, nerves began to fray.
But with an hour gone, there were huge questions being asked as the Rugby Park outfit were awarded a penalty out of nothing.
Foster was penalised after Clancy had touched the ball away in the corner of the area and if any contact was made it was certainly minimal.
Even so, the award stood and Hamill fired in an equaliser despite McGregor diving the right way as he tried to save.
Almost immediately, Smith’s men were denied a kick from 12 yards at the other end as Jelavic fell under Sissoko’s challenge and temperatures began to rise.
Indeed, referee Alan Muir appeared to be struggling as tempers threatened to spill over on both sides with play becoming more and more fraught.
As Killie sunk back into their own half, Foster tried to make amends for conceding the penalty with a drive which flashed over.
After Davis sent a free kick two yards two high, Smith threw on both Lafferty and Weiss as he went for the jugular.
They replaced Diouf and Foster and within moments the SPL champions had another penalty claim waved away.
This time they had good reason to feel aggrieved after Bougherra’s cross struck Clancy’s hand in the area.
Time was beginning to run out but with seven minutes left, Rangers fans thought they finally had a breakthrough when Bougherra nodded in.
He was a yard offside though when Davis played the ball to him and linesman Stephen Mitchell was right to flag.
But just as it seemed it wasn’t going to be the title holders’ day, they edged ahead on 86 minutes.
There was a touch of fortune about the goal as Clancy poked into his own net when Weiss crossed with the outside of his boot rather than cut inside.
But it was the first piece of luck the Light Blues had had all day and it put them back in front at such a crucial time.
Predictably, Killie threw everything they could at the home goal in the closing stages and Jelavic and Papac were both booked as Gers hung on.
In the end, they did just enough and who knows how important this hard-fought victory could be come the end of the campaign.