The home side took the lead through Sam Dalby after 20 minutes, but goals from Mohamed Diomande, Robin Propper and Cyriel Dessers secured three points on the road for Rangers.
From midweek against Manchester United there were four changes as Clinton Nsiala, Mohamed Diomande, Ianis Hagi and Cyriel Dessers all came in, with Leon Balogun, Connor Barron, Ridvan and Vaclav Cerny out of the matchday squad through injury.
That meant Rangers started at Tannadice with Jack Butland in goal behind a back four of James Tavernier, Robin Propper, Clinton Nsiala and Jefte.
Mohamed Diomande came back into midfield after his midweek suspension to line-up alongside Nico Raskin and Nedim Bajrami, while Ianis Hagi supported Hamza Igamane and Cyriel Dessers in attack.
There was a place in the matchday squad for the first time for January signing Rafael Fernandes as was named on the bench alongside Liam Kelly, Tom Lawrence, Leon King, Ross McCausland, Bailey Rice, Zak Lovelace, Findlay Curtis and Paul Nsio.
It was an open start to the game at Tannadice, and the home side almost had a goal inside the first 5 minutes as Sam Dalby looked to head into the bottom left-hand corner from a Ryan Strain corner, but it came off the post before being cleared by James Tavernier.
Dundee United were looking to take advantage of a positive opening spell as Kai Fotheringham shot wide with a right-footed strike across goal shortly after.
Igamane fired an effort over for Rangers as Clement’s men looked to find their rhythm in the opening period in Dundee after a good bit of individual play from the Moroccan to set up the shot.
The home side were continuing to threaten and Jack Butland pulled off a fantastic save to deny Luca Stephenson. The Dundee United man got on the end of a Glenn Middleton cross and drilled a low shot towards the target, but Butland matched the shot with a strong hand.
However, with 20 minutes played, it was the home side who took the lead with Rangers unable to deal with a ball inside the box. The long throw initially came into the area, and Rangers appeared to have a number of opportunities to react and clear the danger, but the ball fell for Dundee United’s on-form striker Sam Dalby and he made no mistake in sending a powerful strike beyond Butland to give his side the lead.
Rangers were back level before the break though, and it was a fantastic strike from Mohamed Diomande with 37 minutes on the clock. Ianis Hagi did well down the right to keep the ball in play, before finding James Tavernier who in turn fed it inside to the midfielder. Diamonde took a touch to open up space for himself before sending a superb right-footed striker across the goal and into the back of the net at Jack Walton’s right-hand post.
Another good chance followed for United as Ryan Strain’s cross was headed towards goal by Fortheringham but the ball was blocked by Butland before Propper cleared.
It was a lively end to the first-half, with Ianis Hagi delivering a dangerous ball across the face of goal which was just ahead of Cyriel Dessers, before Nico Raskin saw his long-range strike deflected wide for a corner
Hagi’s initial corner was cleared by the home side, before it came back to the Romanian, but he could only find the side netting with a shot from a tight angle. In first-half injury time, Walton pulled-off a fantastic double save to deny Cyriel Dessers and Nedim Bajrami to see the sides go in level at the break.
Early in the second-half, Dalby tried to curl a low right-footed strike beyond Butland, but it was a comfortable save for the Rangers goalkeeper before at the other end Hamza Igamane and Cyriel Dessers linked up well with the latter seeing a shot turned behind for a corner.
Just four minutes after the break, Rangers had the lead, and it was Robin Propper who came up with the goal. Still in an advanced position from an earlier corner, Ianis Hagi found the centre back inside the box and he took a touch before sending a powerful strike beyond Walton.
A bit of luck fell Rangers’ way with 20 minutes of the game remaining as a dangerous Dundee United cross across the face of goal was turned towards goal by Nico Raskin but fortunately came back off the post and the danger was cleared.
Rangers were in control in the second half and had the ball in the net again through Cyriel Dessers, but the goal was disallowed for offside in the buildup.
Clement turned to his bench for the first time of the afternoon with less than 10 minutes remaining as Zak Lovelace was introduced in place of Ianis Hagi.
That third goal did come for Rangers, and it was a fine finish for Cyriel Dessers to end off a superb move. It was Zak Lovelace who provided the assist for the Rangers number nine after he was played in by Nedim Bajrami. The youngster showed awareness to find the striker alongside him and Dessers sent a blistering strike high into the back of the net for his sixth goal in four games.
In added time, Rangers were denied by the woodwork as Diomande came close to getting his second goal of the afternoon.
Mohamed Diomande was shown a red card deep into injury time for an altercation with Kevin Holt, and after being called to the screen by VAR, Nick Walsh stuck with his decision and reduced Rangers to 10 men.
RANGERS: Butland, Tavernier, Propper, Nsiala, Jefte, Diomande, Raskin, Bajrami (Nsio, 89), Hagi (Lovelace, 85), Igamane, Dessers.
Subs: Kelly, Lawrence, Fernandes, King, McCausland, Rice, Curtis.
Dundee United: Walton, Strain, Holt, Sevelj, Ferry, Middleton (Van der Sande, 81), Stephenson (Fiorini, 81), Fotheringham (Trapanovski, 63), Dalby, Paton (Moult, 63), Gallagher.
Subs: Richards, Graham, Babunski, Adegboyega, Cleall-Harding.