An early Ryan Jack goal had Philippe Clement’s side ahead at half-time, before Danilo, Sam Lammers, Cyriel Dessers and James Tavernier added to the scoring in the second-half.
There were four changes from Sunday’s win against Hearts at Ibrox as Leon Balogun, Ryan Jack, Scott Wright and Danilo came into the starting XI.
For Balogun, it was just his second league start of the season as he lined-up alongside Connor Goldson at centre-back, with James Tavernier and Ridvan completing the back four in front of goalkeeper Jack Butland.
Ryan Jack came into midfield alongside John Lundstram and Sam Lammers, while Abdallah Sima and Scott Wright joined Danilo in attack.
There was a 45 minute delay to kick-off due to severe traffic disruption in and around the Dundee area. The action got underway at 8.30pm as Rangers looked to make it three wins from three under Clement in the league, while the home side were hoping to maintain their 100 per cent record at Dens Park this season.
It was a disruptive start to the match, and just a few minutes into the game, the players were taken off the field by referee Kevin Clancy due to a fire alarm at Dens Park.
Around 20 minutes later, both teams returned to the field for the match to get underway.
With four minutes played, Rangers had their first chance as a lovely one-two between Abdallah Sima and Ridvan saw the former take a shot at goal but it was just wide of the target.
However, It wasn’t long until Philippe Clement’s men had the opening goal with just five minutes played. Leon Balogun made a fantastic run forward from centre-back as he drove deep into the Dundee half before picking Danilo out with a lovely ball forward.
The Brazilian’s initial strike was blocked by Dundee goalkeeper Trevor Carson, but Ryan Jack was on hand to follow-up on the rebound to give Rangers the early lead and net his first goal of the Scottish Premiership season.
From a corner, the home side had their first chance of the match as Ricki Lamie got a header away at goal but it was just wide of the target.
It was a lively affair from the restart, with Sam Lammers coming close with a right-footed shot after good play from Scott Wright as Rangers looked to build on their early advantage.
Trevor Carson pulled-off a good save to deny Danilo a goal as he got on the end of a free-kick from James Tavernier, but the Dundee goalkeeper matched the effort with an impressive close-range block.
Danilo was denied again by Carson just after the half-hour mark after some good build-up play from Rangers saw the ball land for the striker in the box but once again the keeper was out quickly to block the shot.
Butland was called into action at the other end, as Amadou Bakayoko guided a low strike towards goal after a one-two with Malachi Boateng but the Rangers keeper was on hand to gather, before the linesman raised his flag for offside.
Early in the second-half, Rangers had a good opportunity for their second goal of the match as the Light Blues broke forward from a Dundee chance at pace as Danilo took a good touch to beat the defenders and race through on goal. The striker looked to lift a ball over the goalkeeper, but his effort was just high of the target.
However, it wasn’t long until the striker had his goal as Rangers doubled their advantage in the 51st minute as he made it two goals in the last two games.
Scott Wright picked the ball up on the edge of the box, before a lovely touch from Sima directed it into the path of Danilo who cooly dispatched a right-footed shot beyond Carson.
The home side had a good chance to get one back as Luke McCowan’s shot was blocked by Jack Butland before the Rangers keeper managed to recover well to get a fantastic block on a close range rebound effort from Amadou Bakayoko.
With half an hour of the game remaining, Rangers made their first substitution of the evening as Todd Cantwell was introduced in place of Abdallah Sima.
Rangers were pushing for a third in Dundee, as Danilo saw a low shot deflected just wide of the post.
From a Ridvan corner, John Lundstram’s effort fell for Danilo just in front of goal but Carson, not for the first time this match, pulled off another good save to deny the striker.
With 15 minutes of the match remaining, Rangers’ pressure was rewarded with a third goal, and it was a fantastic strike from Sam Lammers. Danilo was involved as he played the ball to the Dutchman on the edge of the box, and he took a touch onto his left-foot before curling a fantastic strike beyond Carson.
Following the third goal, Clement made two further changes to his side as Cyriel Dessers and Jose Cifuentes were introduced in place of Danilo and Ryan Jack.
There was a fourth goal for Rangers as Cyriel Dessers got on the scoresheet with a lovely finish. Sam Lammers released the striker, and he showed great composure to drive towards goal before finishing beyond Carson.
With a minute left of the 90, a VAR check saw Rangers awarded a penalty as captain James Tavernier was fouled in the box. The skipper stepped up to the spot and made no mistake in firing beyond Carson for the fifth goal of the evening.
RANGERS: Butland, Tavernier, Goldson, Balogun, Ridvan, Lundstram, Jack (Cifuentes, 76), Lammers (Dowell, 85), Sima (Cantwell, 60), Wright (McCausland, 85) , Danilo (Dessers, 76).
Subs: McCrorie, Dowell, Sterling, Barisic, King, McCausland.
Dundee: Carson, Beck, Shaughnessy, Tiffoney (Rudden, 46), Bakayoko (Pineda, 79), Lamie (Kerr, 46), McCowan (Cameron, 85), Boateng (Howley, 72), Donnelly, Sylla, Portales.
Subs: Legzdins, McGhee, Cameron, Reilly, Robertson.