Lachlan Rose gave the home side the lead at Tannadice in the first-half, before Derek McInnes’ men responded through Thelo Aasgaard after the break.
Rangers started with Ivor Pandur in goal behind a back four of Dujon Sterling, Ben Godfrey, Emmanuel Fernandez and Tuur Rommens.
Cammy Devlin made his Rangers debut in midfield as he partnered Mohamed Diomande, with Thelo Aasgaard operating in an advanced role.
Djeidi Gassama provided width in the team, with Ryan Naderi and Lawrence Shankland were named as the two strikers.
It was Rangers who got the action underway and it was a positive start with the first chance coming after just four minutes.
Thelo Aasgaard started the move as he drove forward creating space before finding Ryan Naderi in front of him. He crossed it to Shankland who tried a neat backheel towards goal but it was deflected wide for a corner.
From the resulting set-piece Cammy Devlin dragged a shot just wide from distance in a good spell of early pressure from Rangers.
Naderi was next to get a shot away as he hit a first-time right footed strike after picking up on a loose ball in the box but it was gathered by Jack Walton.
Emmanuel Fernandez made a great tackle at the other end to deny Lachlan Rose a clean shot at goal. The Dundee United man raced through after being fed a pass by Vicko Sevelj, but Fernandez got the crucial touch to take it out of reach of the striker.
Walton pulled off a strong save to deny Rangers an opener as the game approached the half-hour mark as Dujon Sterling delivered an inviting ball into the box. Naderi sent a header towards goal which looked to be creeping in at the post but the Dundee United number one got enough on it to tip it wide.
Emmanuel Agyei saw a shot deflected wide, before Dujon Sterling tried an effort from distance at the other end as he cut inside from the right but it was just wide of the post.
It was the home side who got the opening goal with 38 minutes played at Tannadice. A ball into the box by Jesse Randall crossed into the box, with Lachlan Rose getting enough of a touch to send it beyond Ivor Pandur.
There was a double change for Rangers at the break as Dan Neil and Youssef Chermiti were introduced in place of Ryan Naderi and Djeidi Gassama.
Emmanuel Fernandez came close to levelling as he sent a header on target from a Dan Neil cross but it was saved by the goalkeeper.
Aasgaard was next to send a blistering shot from distance which looked set to nestle in the back of the net but Walton pushed wide.
Rangers had the equaliser they needed and it was a big goal from Thelo Aasgaard in the 56th minute. He picked up on a loose ball inside the box and he took a great touch to create the space before sending a left-footed strike into the back of the net.
There was another change for Rangers with less than half an hour remaining as Ross McCrorie replaced Ben Godfrey, with Dujon Sterling moving into centre-back and McCrorie taking up the right-back slot.
Randall had a chance for the home side as he got on the end of a Bennie pass in space, he tried to curl it round Pandur, but the Rangers number one gathered.
Chermiti had a shot blocked by the goalkeeper in the final minutes, but Gers were unable to find that crucial second goal.
RANGERS: Pandur, Sterling, Godfrey (McCrorie, 63), Fernandez, Rommens, Diomande, Devlin (Curtis, 82), Aasgaard, Gassama (Neil, 46), Naderi (Chermiti, 46), Shankland.
Subs: Kelly, McCrorie, Makhanya, Dragojevic, Chukwuani, Miovski.
Dundee United: Walton, Esselink (Iovu, 63), Sevelj (Camara, 77), Sapsford (Metsoko, 77), Tait, Ferry, Agyei, Rose (Bennie, 70), Forbes, Randall, Rawlins.
Subs: Amissah, Graham, Merghem, Eskesen, Farrugia.