Steven Gerrard's side started well this time and were ahead in the 19th minute, and they kept their 15th clean sheet of the season despite a spirited second-half showing from the hosts.

The result increased the pressure on champions Celtic, who now have two games in hand.

Gerrard made five changes with Alfredo Morelos in for his first start in three matches after equalling Ally McCoist's European goalscoring record with the winner off the bench against Lech Poznan, his 21st goal for the club in the Europa League.

Cedric Itten was handed his third Rangers start in the inside right position behind Morelos.

Despite regular changes to their starting line-up, Rangers are bringing an intensity to the opening stages of games and they took control from the start with Joe Aribo firing just over from 20 yards.

They opened the scoring inside the first 20 minutes for the seventh time in eight league games after referee Andrew Dallas was left with no option but to point to the spot.

Connor Goldson headed on Borna Barisic's free-kick and the ball hit Ross Millen's raised hand. Tavernier put his well-struck penalty into the corner of the net.

Killie barely got near the Rangers penalty area inside the opening half hour but they then started to look more threatening, although Allan McGregor comfortably saved long-range efforts from Stuart Findlay and Chris Burke.

Rangers also dealt with a couple of crosses and they had chances to extend their half-time lead. Goldson headed Tavernier's inswinging corner across the face of goal and Aribo saw his shot deflected just wide after Ryan Kent's knockdown.

The game opened up immediately after the break as Kilmarnock tried to get more support for striker Nicke Kabamba and took more risks.

Kent twice got away down the left and put decent balls in but Rangers could not test goalkeeper Danny Rogers.

Alan Power created a shooting chance at the other end with some great skill but McGregor clutched his left-footed volley.

Millen denied Morelos with a last-ditch challenge before Rory McKenzie had McGregor scrambling with a well-hit long-range volley which fizzed just past.

Rogers pulled off a point-blank stop from Itten following a cross to the back post from substitute Steven Davis as the game continued to be finely balanced.

Kilmarnock boss Alex Dyer brought on Eamonn Brophy, who netted in three wins over Rangers in the previous two seasons, and the striker got a chance with six minutes left after being brought down on the edge of the box.

Brophy drilled a low free-kick but McGregor got his body behind it and pushed it out of the danger zone.

Kirk Broadfoot joined Brophy up front amid a torrential downpour and the former Ibrox defender headed not far wide before Rangers saw out the closing stages without further scares.