There were chances for both sides in Ayrshire, but it was the home side who came up with the crucial breakthrough on the 86th minute to take the three points.
From the last game against St Johnstone, Tom Lawrence and Connor Barron returned to the starting line-up, with Nico Raskin and Ross McCausland on the bench.
Rangers started at Rugby Park with Jack Butland in goal behind a back four of captain James Tavernier, Robin Propper, John Souttar and Jefte.
Connor Barron and Mohamed Diomande were joined in midfield by Tom Lawrence, while Cyriel Dessers led the line once again with support from Vaclav Cerny and Nedim Bajrami.
Prior to the international break, Rangers were on good form domestically, with four victories on the bounce, but Kilmarnock were on a run themselves, losing only once at Rugby Park this season.
There was an early chance for the home side as Kyle Vassell managed to get to the ball ahead of Robin Propper and Jack Butland to get enough on it to tip into the path of Marley Watkins. The Kilmarnock forward was able to get a shot away at goal, but it was cleared by John Souttar.
Shortly after, a dangerous cross was sent across the face of goal by Corrie Ndaba on Kilmarnock’s left-hand side, and was just inches away from Matty Kennedy who, thankfully for Rangers, was unable to get a touch.
At the other end, Cyriel Dessers was in a good position to get on the end of a nice ball from James Tavernier. The striker turned well under the attention of Robbie Deas, but was unable to get a shot away as Robby McCrorie was out to gather.
McCrorie was called into action again with 18 minutes on the clock as he got a strong hand to a powerful strike from Vaclav Cerny to push away an effort from the Czech winger.
The home side thought they had the advantage with almost half an hour played. A short free-kick resulted in Matty Kennedy whipping the ball into the box with Deas sending a header beyond Butland but the linesman raised his flag for offside. Following a VAR check, the goal was disallowed, but it was a warning for Rangers.
Killie captain Kyle Vassell had another chance before the break as a long goal kick from McCrorie reached the striker, and he controlled it well but was unable to keep his effort down as it drifted over Jack Butland.
Early in the second-half, Rangers had a period of pressure as they looked for the breakthrough in this match. Cyriel Dessers struck a powerful low shot towards goal from distance but it was tipped wide by Robby McCrorie at his right-hand post.
From the resulting corner, Dessers struck the bar before Robin Propper’s rebound attempt at the near post was over the target.
Bajrami was next to try a shot from inside the box after a good bit of build-up play from Rangers but it was high of the target from the Albanian international.
With just over an hour played, Clement turned to his bench for the first time as Nico Raskin and Leon Balogun came on in place of Connor Barron and Robin Propper, who had picked-up a knock.
Rangers had a chance from a corner as Robby McCrorie blocked a shot from John Souttar, before Matty Kennedy broke at the other end to race one on one with Jack Butland but the Gers number one matched the shot with a good save.
Another change followed for Rangers, with Hamza Igamane coming on in attack, replacing Cyriel Dessers for the final 20 minutes.
With both teams still searching for the breakthrough, there were another two changes for Rangers as Kieran Dowell and Neraysho Kasanwirjo came on for Tom Lawrence and Vaclav Cerny.
There was disaster for Rangers with 86 minutes played at Rugby Park, a ball from midfield from David Watson was sent forward to Marley Watkins and the Kimarnock forward managed to touch it beyond Butland and into the back of the net.
With six minutes added time, Clement’s men were looking to rescue something from the game. A chance did come, and it was just inches wide from Hamza Igamane as his low strike from a tight angle beat McCrorie but drifted wide of the post.
RANGERS: Butland, Tavernier, Propper (Balogun, 61), Souttar, Jefte, Barron (Raskin 61), Diomande, Lawrence (Dowell, 79), Bajrami, Cerny (Kasanwirjo, 79), Dessers (Igamane, 72)
Subs: Kelly, McCausland, Fraser, McKinnon.
Kilmarnock: McCrorie, Ndaba, Mayo, Deas, Lyons, Vassell (Anderson, 72), Kennedy (McKenzie, 90), Armstrong (Mackay-Steven, 72), Findlay, Donnelly (Watson, 86), Watkins (Burroughs, 90).
Subs: O’Hara, Murray, Wales, Bainbridge.