Barry Ferguson’s men were 3-1 down with half an hour remaining at Dens but turned things around in remarkable fashion with goals from James Tavernier, Tom Lawrence and Dessers securing the victory.
There was just one change from the Old Firm derby as Hamza Igamane came in from the start in place of the injured Vaclav Cerny.
That meant Rangers lined-up with Jack Butland in goal behind James Tavernier, John Souttar, Leon Balogun, Dujon Sterling and Ridvan.
In midfield, Nico Raskin and Mohamed Diomande, who both impressed on international duty, retained their places alongside Connor Barron, while Cyriel Dessers joined Hamza Igamane in attack.
It was not the start Rangers were looking for at Dens, with the home side opening the scoring inside two minutes. Finlay Robertson delivered a ball into the box from the first corner and Simon Murray managed to get on the end of it in a central area to guide a looping ball into the back of the net and beyond Butland.
Dessers had an opportunity for Rangers to respond quickly in the 6th minute but the striker was just wide of Carson’s left-hand post with his effort.
The forward was continuing to threaten, and forced a good save from Carson as he raced through on goal but his shot was blocked by the feet of the Dundee goalkeeper.
With 19 minutes played, it was the home side who had the ball in the back of the net once again. Joe Shaughnessy’s initial header was spilled by Jack Butland with Simon Murray following up on the rebound.
Butland blocked Murray’s effort, but Shaughnessy followed up and this time the Dundee captain was able to convert to double their advantage.
Oluwaseun Adewumi had another opportunity for the home side as he raced through on goal, but Dujon Sterling defended well to deny the forward a clear shot as he got his body in the way to send the ball out for a Dundee corner.
With the game approaching half-time, Ferguson’s men continued to search for a crucial goal as Igamane was next to test Carson with a shot which the goalkeeper matched with a diving save, before Dessers’ header was cleared off the line by Simon Murray from the resulting corner.
The goal did come, and it was a bit of fortune for Gers as James Tavernier’s delivery into the box was turned into the back of his own net by Joe Shaughnessy.
It gave Rangers a lift, and Carson was called into action shortly after as he denied Dessers with another good save. In the final minute of the first-half, there was another big opportunity for the Rangers striker but Carson once again blocked his shot from close range.
Ferguson turned to his bench at half-time, with Ianis Hagi and Bailey Rice introduced in place of Leon Balogun and Connor Barron.
Igamane flashed a shot inches wide of the target in the opening minutes of the second-half as Rangers looked to start where they left off. However, the home side were still threatening too as Mulligan’s dangerous ball into the box was sent wide by Tiffoney at the back post.
It was a lively start to the second-half and Rangers thought they had the equaliser with 50 minutes played as Dessers found the back of the net with a nice finish but it was disallowed for offside.
Another change followed with Jefte coming on for Ridvan for the remaining half an hour at Dens.
With 62 minutes on the clock, Dundee had their third of the evening, as Scott Tiffoney made up for his earlier opportunity by driving towards goal before opening up space and sending a powerful right-footed shot into the back of the net to give Dundee a 3-1 lead.
Ferguson turned to his bench instantly with Danilo coming on in place of Hamza Igamane before Tom Lawrence was introduced for Diomande shortly after.
Rangers kept pushing and had another goal back with 76 minutes played in Dundee. Danilo laid the ball off to James Tavernier and the captain released a fantastic shot from distance beyond Carson.
Five minutes later, Rangers were level and it was another fine strike from distance, this time from substitute Tom Lawrence. He received the ball from Nico Raskin on the edge of the box and sent a right-footed shot beyond Carson to draw the Light Blues level.
Simon Murray hit the post for Dundee in added time, but it was Rangers who got the winner.
With 93 minutes on the clock, Dessers marked his 100th appearance for the club in spectacular fashion as he got on the end of a long ball from James Tavernier to chest in down and give Rangers the late lead.
RANGERS: Butland, Tavernier, Souttar, Balogun (Hagi, 46), Ridvan (Jefte, 60), Sterling, Raskin, Barron (Rice, 46), Diomande (Lawrence, 73), Igamane (Danilo, 64), Dessers.
Subs: Kelly, Propper, Cortes, Bajrami.
Dundee: Carson, Shaughnessy, McGhee, Tiffoney, Mulligan, Adewumi, Murray (Reilly, 89), Robertson (Garza, 65), Larkeche, Sylla, Donnelly.
Subs: McCracken, Sharp, Ingram, Astley, Samuels, Koumetio, Lopez