Match ends, Rangers 1, Kilmarnock 0.
Rangers stay five points behind Scottish Premiership leaders Celtic as Alfredo Morelos came off the bench to break stiff Kilmarnock resistance.
Morelos was named among the substitutes on his return from suspension as manager Steven Gerrard stuck with the starting XI that defeated Hibernian.
Rangers had most of the chances only to be thwarted by the crossbar and goalkeeper Laurentiu Branescu.
But Morelos fired home seven minutes after coming on after the break.
It means Rangers, now unbeaten at Ibrox in nine games and with a game in hand over their city rivals, head to Celtic Park on Sunday after three consecutive wins without losing a goal.
Kilmarnock have dropped to sixth, have now lost four in a row, having not won in six, not scored in five and not won away from home in four.
Back to future Kilmarnock frustrate
Both managers sprung surprises ahead of kick-off, with Gerrard leaving top scorer Morelos on the bench.
Whether sticking with the same starting XI was a reward for Friday's convincing win at Easter Road or with one eye on the forthcoming Old Firm derby, it also meant that Steven Davis also had to make do with a place among the substitutes on his return from injury.
Gerrard had guessed in his pre-match interview that, after the sacking of Angelo Alessio, Kilmarnock caretaker boss Alex Dyer would return to the more conservative approach deployed under Steve Clarke - a strategy that meant the Ayrshire side had only lost once in five league visits to Ibrox.
So it turned out as Dyer dropped Scotland striker Eamonn Brophy and veteran former Rangers winger Chris Burke to the bench to rely on the speed of on-loan Liverpool forward Liam Millar as his lone out-ball.
Rangers initially continued where they left off in Edinburgh, with Jermain Defoe having an effort deflected wide and Nikola Katic firing past a post within the opening minutes.
Clarke's philosophy was to be difficult to beat while making the best of your own chances and Niko Hamalainen came close to doing just that as the Finland full-back's shot deflected wide off James Tavernier on a rare foray into Rangers' half.
As Borna Barisic fired straight at Kilmarnock goalkeeper Laurentiu Branescu, Connor Goldson's goal-bound header deflected off team-mate Defoe and Glen Kamara's snap shot clipped the crossbar, Rangers' frustration deepened as the wall of nine yellow jerseys behind striker Millar stood firm by half-time.
Branescu was proving a stubborn barrier and, when Kilmarnock's Alan Power forced Allan McGregor into a save on the break, Gerrard responded by sending on Morelos for Defoe.
The Colombian's 28th goal of the season was to follow soon after as he finished off a sweet passing move involving Ryan Jack and Joe Aribo.
A few more chances, a few nervous moments at the other end, but Gerrard's gamble paid off and Morelos heads to Celtic Park fit, free of suspension and brimming with confidence ahead of what could prove a decisive game in the title race.
'Sorry if it didn't look pretty' - reaction
Rangers manager Steven Gerrard: "Killie set us a challenge, come and beat us and they made it very difficult for us. We found a way, which is very pleasing.
"I apologise if it didn't look pretty for the supporters, that it wasn't three, four or five goals. But I'm going away very happy because it's a win and a clean sheet."
Interim Kilmarnock manager Alex Dyer: "We were outstanding. Everyone worked hard, they were confident, I was chuffed with them - very pleased.
"We knew what kind of game it was going to be. It was just about us having discipline and sticking to a game plan and hopefully we would create a couple of opportunities - which we did do."
- 37ArfieldSubstituted forStewartat 64'minutes
- 9DefoeSubstituted forMorelosat 58'minutes
- 14KentSubstituted forDavisat 78'minutes
- 22MillenSubstituted forBurkeat 68'minutes
- 26Del Fabro
- 4BruceBooked at 66mins
- 20WilsonBooked at 10mins
- 15El MakriniSubstituted forThomasat 84'minutes
- 11MillarBooked at 47minsSubstituted forBrophyat 63'minutes
- Steven McLean
- Shots on Target
Second Half ends, Rangers 1, Kilmarnock 0.
Foul by Alfredo Morelos (Rangers).
Gary Dicker (Kilmarnock) wins a free kick in the defensive half.
Attempt saved. Joe Aribo (Rangers) left footed shot from the centre of the box is saved in the top right corner. Assisted by Greg Stewart.
Attempt missed. Greg Stewart (Rangers) left footed shot from outside the box is high and wide to the left. Assisted by Glen Kamara.
Foul by Alfredo Morelos (Rangers).
Rory McKenzie (Kilmarnock) wins a free kick in the defensive half.
Nikola Katic (Rangers) wins a free kick in the defensive half.
Foul by Eamonn Brophy (Kilmarnock).
Foul by Greg Stewart (Rangers).
Niko Hämäläinen (Kilmarnock) wins a free kick in the defensive half.
Alfredo Morelos (Rangers) wins a free kick in the defensive half.
Foul by Alan Power (Kilmarnock).
Foul by Nikola Katic (Rangers).
Eamonn Brophy (Kilmarnock) wins a free kick in the attacking half.
Substitution, Kilmarnock. Dom Thomas replaces Mohamed El Makrini.
Attempt missed. Joe Aribo (Rangers) left footed shot from very close range is close, but misses to the right. Assisted by James Tavernier.
Attempt saved. Nikola Katic (Rangers) header from the centre of the box is saved in the top right corner. Assisted by Borna Barisic with a cross.
Corner, Rangers. Conceded by Dario Del Fabro.