Gavin Rae scored his first Rangers goal as Dundee were brushed aside at Ibrox.
Peter Lovenkrands celebrates the opening goal
Peter Lovenkrands blasted home from close range late in the first half and Frank de Boer powered in a free kick shortly after the interval.
Rangers were on top for long spells and added to their lead in the 81st minute when Rae shot home from the edge of the penalty area against his old side.
Steven Thompson caught the eye up front for Rangers and was rewarded with the final goal in the 83rd minute.
Rangers started in brisk fashion and a Michael Ball shot from 25 yards whizzed across goal and just wide.
But there was a lucky escape for the home side in the 10th minute when Rangers skipper Craig Moore could only head a long ball into the path of Nacho Novo but the striker pulled his shot wastefully wide.
Lovenkrands was next to threaten for Rangers when he stole in at the back post to meet a cross from teenage full-back Alan Hutton but the Dane steered the ball inches wide.
Dundee were given a fright when defender Tom Hutchison knocked a sloppy back-pass beyond Julian Speroni but the goalkeeper was able to recover and kick the ball to safety.
Dundee were camped around their own penalty box as Rangers poured forward and moved the ball around nicely with some one-touch play.
Speroni tipped over a close range header from Lovenkrands and produced another great save to keep out a powerful downward header from Steven Thompson.
Former Dundee midfielder Rae appeared to have opened the scoring against his old side when he was given time and space to send and angled shot beyond Speroni but Dave Mackay made a sliding block on the goal-line.
From the resulting corner Michael Mols, on for the injured Ronald de Boer, saw his header cleared by Steven Robb, who was guarding a post.
Rangers' pressure paid off in the 41st minute when Lovenkrands knocked the ball home from close range.
Dundee struggled to clear their penalty area and Frank de Boer beat Speroni to a looping ball and headed into the goalscorer's path.
Linesman James Bee was waving his flag but referee Alan Freeland ruled that the goal was legitimate.
Lovenkrands knocks in the first goal of the game
Neil Barrett brought Rae tumbling down in the 47th minute and Frank de Boer scored from the free kick.
Speroni got a hand to the Dutchman's 25 yard curling shot and will be disappointed not to have kept it out.
Ball's corner found the head of Bob Malcolm inside the six-yard box and but the half time substitute failed to hit the target.
Rangers continued to dominate and substitute Chris Burke was full of dangerous running.
With ten minutes remaining Dundee again made a mess of clearing their lines and the ball dropped to Rae, who blasted home a fine shot from 18 yards for his first Ibrox goal.
Two minutes later Thompson produced a cool finish once Mols had flicked a Hutton cross in his direction.
Rangers: Klos, Khizanishvili, Moore, Frank de Boer, Hutton, Hughes, Rae, Lovenkrands, Ball, Ronald de Boer, Thompson. Subs: Mols, Malcolm, Vanoli, Burke, McGregor.
Dundee: Speroni, Mackay, Mair, Hutchinson, Hernandez Santos, Fotheringham, Sancho, Barrett, Robb, Novo, Kneissl. Subs: Milne, Lovell, Brady, Cameron, Soutar.
Referee: A Freeland