Going ahead through a quite incredible James Tavernier free-kick, the home side equalised through Lewis Smith before Connor Goldson grabbed what proved to be the winner just before half-time.
From the side which defeated Lech Poznan on Thursday night to top Europa League Group D, in came goalkeeper Allan McGregor, skipper James Tavernier, Steven Davis, Ryan Kent, Kemar Roofe and Alfredo Morelos.
The six players to switch out of the side today – Jon McLaughlin, Ianis Hagi, Cedric Itten, Bongani Zungu, Nathan Patterson and Joe Aribo – were all on the bench, with manager Steven Gerrard once again having a strong pool to pick from.
The visitors began the first half shooting up the famous Tannadice slope on what was a pretty soft surface given recent weather.
It was the home side who had the first opportunity of the game on nine minutes – a corner from Adrian Sporle ricocheted around the area before finally dropping to Mark Reynolds 14-yards out, but Kemar Roofe was there with a block to get it away to safety.
Gers responded with Alfredo Morelos picking up in midfield, driving for goal and letting fly with a decent 25-yard effort which only just slipped past the left-hand post.
Roofe was then inches away from connecting to a great Scott Arfield ball with his head, before on 26 minutes, Rangers hit the front with a simply stunning free-kick from James Tavernier.
Fully 30-yards from goal in a central area, both the captain and Borna Barisic stood over the ball. It seemed one of the two full-backs would simply try and drop it onto the head of one of the gathered cluster of blue shirts who had come forward.
Tavernier, however, had other ideas. As perhaps another sign of the confidence he is playing with at the moment, he took on the strike and with incredible precision and power, found the top-left corner and out of reach of the despairing Benjamin Siegrist in goal for United.
It was his 17th goal of the season – matching his own record for the highest strike rate for a Gers defender.
Roofe came close to a second soon after Kent put him in but United cleared the danger before, on 33 minutes, the home side levelled matters.
Sporle delivered a teasing ball to the back post, and coming in on the end of it to volley home was Lewis Smith.
The visitors quickly got back on the front-foot, and Tavernier had a decent opportunity at the front-post, volleying wide a teasing Kent cross, while Morelos headed over, under some pressure, another cross from the attacker.
Then, on the stroke of half-time, Rangers went back in front.
Tavernier took a super free-kick to deliver into the area this time from the right, and meeting his wonderful ball with a flicked header was Connor Goldson.
It was a brilliant header from the big defender to get the ball across Siegrist for his sixth of the season to send Gerrard’s men in ahead at the break.
Into the second half, and Morelos came close again with an effort from distance, again firing just wide, while Leon Balogun got on the end of a Borna Barisic free-kick into the area, nodding down for Goldson who fired over.
Roofe then playing a stunning ball in for Morelos, who was eight-yards out. He couldn’t sort his feet out, however, and by the time Tavernier arrived to try and poke the loose ball home, Siegrist was on the scene to claim the ball.
Goldson then had another header, this time from a corner, deflected over, while sub Cedric Itten was fed to run clear on the right, with Siegrist coming out to meet him.
The Swiss striker rounded the ‘keeper and gave it to the incoming Arfield. His shot was on target, but Mark Connolly was on the line to make an excellent block.
Arfield then got on the end of a Barisic front-post corner, but Siegrist blocked – but Gers saw it out with no opportunities conceded at the other end for another three points.
RANGERS: McGregor, Tavernier, Goldson, Balogun, Barisic, Arfield, Davis, Kamara (Zungu, 81), Roofe, Kent (Aribo, 86), Morelos (Itten, 73)
SUBS NOT USED: McLaughlin, Bassey, Helander, Hagi, Defoe, Patterson.
DUNDEE UNITED: Siegrist, Smith, Sporle (Watson, 86), Connolly, Reynolds, McNulty, Edwards, Robson, Harkes, Shankland, Fuchs.
SUBS NOT USED: Deniz, Powers, Appere, Neilson, Hutchinson, Duffy, Smith, Malcolm.
REFEREE: Steven McLean
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