Dundee made a couple of changes when Mo Sylla and Scott Tiffoney started, with Aaron Donnelly and Michael Mellon moving to the bench.
Dundee started well and were going forward with some neat football, but it was Rangers who had efforts at goal with McCracken saved with ease.
After 32 minutes Luke McCowan sent a badly misjudged pass across the face of the Dundee penalty area straight to Ross McCausland. McCracken spared his skipper’s blushes by touching the shot over the bar.
Into the last 10 minutes of the half and all off a sudden Dundee had good efforts on goal as they came close twice. First, Butland held a firmly struck 30 yard shot from Scott Tiffoney. In Dundee’s next attack McCowan played Tiffoney into the penalty area. Butland saved and Tiffoney’s goalbound follow up was headed away by Ben Davies.
The Dark Blues kept attacking and Butland again saved well from Malachi Boateng’s curling 20 yarder.
But minutes later Dundee scored after a neat play across the midfield ended with a Owen Dodgson and he hit a lovely low cross across the face of goal for Jordan McGhee to shoot past Butland at the far post.
Two minutes later the Dark Blues had a free kick wide on the left. McCowan played it short to Dodgson who hit another wicked cross into the danger area and Antonio Portales scored with an cheeky flick off the outside of his boot.
In a crazy period Dundee went close again when Sylla put a effort just wide off the post, but in injury tme Rangers scored to get back into the game.
Second half and it took Rangers 7 minutes to level the score at 2-2. It was all Rangers and after 65 minutes it was 3-2. Dundee struggled to get back into the game.
Silva spun and shot from the edge of the penalty area but McCracken saved well. The Dee keeper then pulled off a magnificent save to keep out a Dessers header.
It was a great save Dundee put on Robertson, Costello and Main to try and get a vital goal but after a ten minute spell they were under more pressure from the home side.
Rangers scored twice more in the final minutes to end the game 5-2. It was a tale of two halfes with Dundee better team in the first half, Rangers controlled the game second half a deserved the win.
The European dream is over and at least Manager Tony Docherty will know now what is needed to get better next season. Last game of the season is when Kilmarnock come to Dens Park on Saturday.
Dundee: McCracken, McGhee, Astley, Portales, Dodgson, Sylla (Robertson 74), Boateng (Mellon 86), Cameron, McCowan, Tiffoney (Costelloe 74), Bakayoko (Main 74). Unused Subs: Sharp (gk), Mulligan, Robinson, Howley, Donnelly.
Referee: Matthew MacDermid
Att: 45,760