Alfredo Morelos scored twice as Rangers recovered from Chris Stokes’ early opener to bring all three points back from Kilmarnock.
Killie started brightly at Rugby Park and pulled into a deserved early lead when Stokes headed home Daniel Armstrong's corner.
The hosts' lead lasted less than 20 minutes, though, with Morelos unmarked at the back post to meet Fashion Sakala's low cross. Kent then gave Rangers the lead soon after the restart.
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Daniel Amstrong was sent off for Killie on the hour and Morelos added a second, with a header, but Joe Wright struck late for the hosts with what ultimately proved to be a consolation.
The win leaves Rangers still nine points behind league leaders Celtic at top of the table. Killie drop to 11th, level on points with Motherwell and Dundee United, although having played a game more.
Rangers come from behind for another victory
In a barnstorming Killie start to the cinch Premiership encounter, defender Stokes headed in from a corner after six minutes only for Rangers' Colombian striker to level midway through the first half.
Kent struck six minutes after the break before Kilmarnock winger Armstrong was sent off by referee Kevin Clancy for picking up the second of two yellow cards for an elbow in the face of left-back Borna Barisic.
Morelos headed in his second from a Barisic cross in the 73rd minute but Killie pulled a goal back in the 85th minute through defender Wright to ensure a nervy ending.
Michael Beale has won seven and drawn one of his eight games as Rangers boss but it was another patchy performance and they remain nine points behind relentless Celtic at the top of the table, with the Hoops beating St Mirren 4-0 at Parkhead.
It was a more difficult night than many Rangers fans would have envisaged against the second-bottom side in the Premiership.
Following a gruelling 2-1 win over Aberdeen on an energy-sapping Hampden Park pitch on Sunday, Beale freshened up his team on a freezing night in Ayrshire by bringing in keeper Jon McLaughlin, Glen Kamara and Scott Arfield.
The home side showed four changes with Stokes, Ryan Alebiosu, Christian Doidge and Liam Polworth returning and they had Rangers in a headlock in the opening minutes and deservedly took the lead.
Rangers failed to heed the warning when centre-back Ash Taylor headed a corner wide of the target before Stokes put his head on Armstrong's delivery to beat McLaughlin.
The visitors were all over the place.
It was the 17th minute before Killie keeper Sam Walker had a real save to make, diving low to beat away a header from Connor Goldson before McLaughlin had to deal with a decent curling effort from Armstrong at the other end.
Rangers steadied a little and got the equaliser when attacker Fashion Sakala raced on to a pass from skipper James Tavernier and squared for Morelos to sweep into the net from eight yards.
Beale's side got off to a good start in the second half with Kent firing in from inside the box after taking a pass from Morelos following a counter-attack.
However, moments after Wright missed a great chance when he headed wide from 12 yards and more woe followed when Armstrong, booked in the first half for pulling back Kent, was sent packing for a needless foul on Barisic.
Rangers pressed to take advantage of their extra man and were rewarded when Morelos rose six yards from goal to head in a chip from Barisic.
Walker denied the Colombian his hat-trick with a decent save in the 78th minute before the Rangers forward was replaced by Malik Tillman.
With five minutes remaining of normal time, Wright volleyed high past McLaughlin after Taylor had flicked on an Alan Power cross and a game in which Rangers controlled became troublesome until three added minutes had passed.
Kent hints at Rangers stay
Rangers winger Ryan Kent speaking to Sky Sports:
"There's no decision yet and I'm just concentrating on the rest of the season, but I'll sit down with the manager to discuss further.
"It's not a distraction for me. I've got full trust in the manager. He's been key for me since I was a young lad and that trust is reciprocated. He's a quality manager."
Beale: Morelos getting back to his best
Rangers manager Michael Beale speaking to Sky Sports:
"He's working very hard for the team, and he's not missed many chances in the previous games but tonight I thought he took both his goals really well. He's a real handful. He'll drag us up the pitch and I thought, again, our front three were very effective in the game."
McInnes: Armstrong red changed the game
Kilmarnock manager Derek McInnes speaking to Sky Sports:
"The game changes with the sending off and from thereon in it was very difficult. Credit to the players. They stuck to the task and kept searching for those moments. I though at least we saw the game out properly in front of the supporters, we had a go as much as we could."
What's next?
The attention now turns to the fourth round of the Scottish Cup this weekend.
Kilmarnock are at home to League Two side Dumbarton on Saturday. Kick-off 3pm.
Rangers are away to St Johnstone in an all-Scottish Premiership tie. That game kicks off at 5.30pm.