Samuel Dalby opened the scoring for the visitors with a header in the first-half, before Rangers responded through Vaclav Cerny.
There were two changes from the last league outing against Hearts as Dujon Sterling and Robin Propper came in from the start, with James Tavernier and Leon Balogun on the bench.
That meant Rangers started at Ibrox with Jack Butland in goal behind a back four of Dujon Sterling, John Souttar, Robin Propper and Jefte.
Nico Raskin, Connor Barron and Mohamed Diomande were once again in midfield, while Vaclav Cerny and Nedim Bajrami supported striker Cyriel Dessers.
Rangers were first to have a shot at target in this match as Vaclav Cerny found space on the edge of the box to release a powerful right-footed strike towards goal but it was gathered by Jack Walton.
At the other end, Ryan Strain managed to get a cross in from the right which fell for Dundee United captain David Babunski who sent an effort just wide of Jack Butland’s left-hand post, before Nico Raskin sent a shot high of the bar as Rangers continued to search for an opening goal.
Raskin came close again shortly after and this time forced a good save from Walton as he reacted to push away the strike.
The Dundee United keeper was called into action again with almost half an hour gone, as Nedim Bajrami found himself in space 25-yards out and released a curling shot which looked to be heading for the back of the net, but Walton got a strong hand to tip it wide.
However, it was the visitors who took the lead at Ibrox with 35 minutes played. A dangerous delivery was swung into the box by Vicko Sevelj with Samuel Dalby in space to head beyond Butland and give his side the advantage. The goal was checked by VAR for a possible offside from the striker, but the header stood.
In first-half injury time, John Souttar got a crucial block on a close-range attempt from Kai Fotheringham as United put pressure on late in the half.
Rangers had the ball in the back of the net late in injury time as Robin Propper headed home, but the goal was disallowed for a handball from Connor Barron in the build-up.
There was a double change for Rangers at the break as Ianis Hagi and Danilo were introduced in place of Mohamed Diomande and Cyriel Dessers.
Early in the second-half, Barron found Souttar at the back post as Rangers looked for a quick response, but there was just too much on it for the defender as he hit the side netting.
Ryan Strain delivered a ball into the box for Dundee United with David Babunski heading towards goal but it was just wide from the captain.
There was an opportunity for Danilo with 55 minutes played. It was good build-up from Rangers as Hagi and Cerny combined well, with the latter cutting the ball into the path of Danilo but the Brazilian’s touch sent it wide of the target.
Cerny was next to try a shot as Rangers continued to push for the equaliser as he flashed a power strike just wide of the target.
The goal did come with 66 minutes played and it was Cerny who came up with the important finish. The move started with the Czech Republic international as he found Danilo, who controlled the ball well on the edge of the box before laying a lovely pass back into the path of Cerny who guided a low shot into the bottom corner beyond Walton.
After the goal, Ridvan was introduced for his first minutes since August after recovering from injury, as he returned to replace Jefte.
Rangers were finding their rhythm and Walton denied Danilo shortly after with a good block before Cerny had the ball in the net again but was flagged for offside.
There was a fantastic opportunity for a winning goal with less than five minutes to go. Ianis Hagi’s shot from 30 yards was pushed away by the keeper, with Danilo’s rebound shot blocked by a defender before Igamane’s follow-up was saved by the keeper.
With eight minutes added on at Ibrox, Clement’s men were continuing to search for the winner.
A corner provided an opening as Cerny’s delivery was headed towards goal by Nico Raskin, but Walton gathered. The Dundee United keeper pulled off a big save in the final minute to tip away a shot from Hamza Igamane as both sides shared the points at Ibrox.
RANGERS: Butland, Sterling, Souttar, Propper, Jefte (Ridvan, 66), Raskin, Barron, Diomande (Hagi, 46) Cerny, Bajrami (Igamane, 79), Dessers (Danilo, 46)
Subs: Kelly, Tavernier, Dowell, Balogun, McCausland.
Dundee United: Walton, Strain, Holt, Sevelj, Babunski, (Van der Sande, 63) Ferry, Middleton, Stephenson, Fotheringham (Thomson, 73), Dalby (Odada, 78), Gallagher.
Subs: Richards, Moult, Adegoboyega, Constable, Stirton, Ubochioma.