Ryan Jack’s strike had the visitors in front at half-time before four goals after the break from Danilo, Sam Lammers, Cyriel Dessers and James Tavernier extended their unbeaten run under new manager Philippe Clement to three games.
Dundee offered little as an attacking force, with Amadou Bakayoko seeing his second-half effort well saved by Jack Butland.
Kick-off was delayed by 45 minutes after the Rangers team bus was caught up in traffic congestion crossing the Tay Bridge.
Play was then suspended not long after kick-off for a further 18 minutes after flares lit by the visiting supporters set off fire alarms in the stand, with referee Kevin Clancy taking the players off the pitch.
Dundee made three changes following their win away to Livingston. In came Ricki Lamie, Bakayoko and Scott Tiffoney, with Jordan McGhee, Lyall Cameron and Zak Rudden dropping out.
Rangers, in turn, made four changes from the team that defeated Hearts. Out went Nicolas Raskin, Todd Cantwell, Ben Davies and Dessers, replaced by Jack, Leon Balogun, Scott Wright and Danilo.
Rangers started brightly when the game finally got going and Abdallah Sima slid a chance just wide after being played in by Ridvan Yilmaz.
The Light Blues, though, moved in front with their next attack. Balogun sent Danilo running in and when Trevor Carson spilled the Brazilian’s cross, Jack was on hand to sweep in the rebound.
Dundee replied through a Tiffoney cross that Balogun did well to head away from danger.
Carson partially redeemed for his error with a point-blank range save from Danilo, although the offside flag would likely have ruled the goal out in any case.
Malachi Boateng then had a go at the other end but Butland, in the Rangers goal, made a comfortable save.
Danilo ought to have put Rangers two in front early after the restart but, after doing well to create a shooting chance from a long ball, he blazed his effort well off target.
He was far more clinical after 51 minutes when the visitors doubled their lead. Sima teed him up and Danilo finished well beyond Carson into the far corner.
At the other end Butland pulled off a double save to deny first Luke McCowan and then Bakayoko as Dundee looked to narrow the deficit.
Instead it was Rangers who pulled away, scoring three more times.
Lammers claimed the first with a stunning long-range effort before teeing up Dessers who finished well despite Dundee protests for a foul in the build-up.
Tavernier claimed the fifth from the spot after Cameron was adjudged to have fouled Dessers.