The visitors' swift, sharp passing and ruthlessness in the final third created goals for Andy Halliday, Jason Holt and the excellent Barrie McKay.
Martyn Waghorn scored two penalties as Rangers made it eight wins from eight.
In the home ranks, striker Derek Lyle was dismissed after going head-to-head with Rob Kiernan, with Aidan Smith netting a late breakaway consolation.
Rangers sought to play with pace from the off, as captain Lee Wallace latched onto the lively McKay's pass at full tilt down the left, surging into the home box, but finding neither a team-mate nor the bottom corner with his bobbling ball across the face of goal.
And McKay was instrumental in Rangers' opener, driving at the defence, exchanging passes with Waghorn, and playing in Halliday to clip the ball across goalkeeper Robbie Thomson.
A knee injury deprived Rangers of their skipper shortly after the half-hour mark, before Hibernian loanee Alex Harris stung the palms of Wes Foderingham in the away goal with a driven strike from the right of the area.
Minutes later Chris Higgins, who had already clattered the speeding James Tavernier early on, allowed Waghorn the opportunity to attack again with an awful looping backwards header in his own half, but made amends with a smart block in the box.
On the stroke of half-time, Ryan Conroy wasted a fine chance for Queens on the break, as he opted to square for Lyle rather than shoot himself, with Danny Wilson sliding in smartly to block.
Three minutes after the break, with Mark Millar booked for treading on the prone Gedion Zelalem, Lyle was dismissed on the advice of fourth official Crawford Allan.
The striker went forehead-to-forehead with Kiernan, and the minimal forward motion he made with his head was in full view of Allan, who advised referee Bobby Madden to show a red card.
If things were not bad enough for Queens, they got worse three minutes later, as Andy Dowie shouldered Dominic Ball to the ground in the box as the midfielder raced to reach Tavernier's square ball with the empty net beckoning.
Right-back Dowie, who had been torn apart by the pace and trickery of McKay during the first half, was only shown yellow.
Waghorn slammed home the resultant spot-kick, and from that point Rangers' high-tempo passing football was too much for the hosts.
Holt ran unchallenged into the Queens area, and finished Zelalem's through ball at the second time of asking to bag the visitors' third.
And more smart, intricate passing from Waghorn and Kenny Miller allowed McKay to tap home a deserved fourth on 65 minutes.
Rangers boss Mark Warburton introduced the flamboyant Nathan Oduwa for the final 20 minutes, with the substitute drawing several fouls from the home defence.
After Oduwa was chopped down on the edge of the area, Iain Russell raised his arm high to block the resultant free-kick, and Waghorn thumped his second penalty beyond Thomson.
Queens did get off the mark in the final 10 minutes, young striker Smith capitalising on a long central punt and holding off Kiernan well to knock the ball past Foderingham.
Match ends, Queen of the South 1, Rangers 5.
Second Half ends, Queen of the South 1, Rangers 5.
Attempt missed. Andy Halliday (Rangers) right footed shot from outside the box is close, but misses to the right from a direct free kick.
Foul by Chris Higgins (Queen of the South).
Martyn Waghorn (Rangers) wins a free kick in the defensive half.
Attempt saved. Fraser Aird (Rangers) right footed shot from the right side of the box is saved in the bottom right corner.
Corner,  Queen of the South. Conceded by Barrie McKay.
Rob Kiernan (Rangers) is shown the yellow card for a bad foul.
Iain Russell (Queen of the South) wins a free kick on the left wing.
Foul by Rob Kiernan (Rangers).
Attempt missed. Martyn Waghorn (Rangers) right footed shot from more than 35 yards is too high from a direct free kick.
Darren Brownlie (Queen of the South) is shown the yellow card for a bad foul.
Foul by Darren Brownlie (Queen of the South).
Martyn Waghorn (Rangers) wins a free kick in the attacking half.
Foul by Aidan Smith (Queen of the South).
Gedion Zelalem (Rangers) wins a free kick in the attacking half.
Andy Halliday (Rangers) wins a free kick in the defensive half.
Foul by Jake Pickard (Queen of the South).
Attempt missed. Nathan Oduwa (Rangers) right footed shot from a difficult angle on the left is close, but misses to the left.
Goal!  Queen of the South 1, Rangers 5. Aidan Smith (Queen of the South) left footed shot from very close range to the bottom left corner. Assisted by Andy Dowie.
Corner,  Rangers. Conceded by Jordan Marshall.
Goal!  Queen of the South 0, Rangers 5. Martyn Waghorn (Rangers) converts the penalty with a left footed shot to the top left corner.
Iain Russell (Queen of the South) is shown the yellow card for hand ball.
Penalty conceded by Iain Russell (Queen of the South) with a hand ball in the penalty area.
Foul by Jake Pickard (Queen of the South).
Nathan Oduwa (Rangers) wins a free kick in the attacking half.
Jake Pickard (Queen of the South) is shown the yellow card for a bad foul.
Foul by Jake Pickard (Queen of the South).
Nathan Oduwa (Rangers) wins a free kick on the left wing.
Foul by Jordan Marshall (Queen of the South).
Gedion Zelalem (Rangers) wins a free kick in the attacking half.
Substitution, Rangers. Fraser Aird replaces James Tavernier.
Foul by Jordan Marshall (Queen of the South).
Gedion Zelalem (Rangers) wins a free kick on the left wing.
Attempt saved. James Tavernier (Rangers) right footed shot from outside the box is saved in the centre of the goal.
Nathan Oduwa (Rangers) wins a free kick in the attacking half.
Foul by Kyle Hutton (Queen of the South).
Substitution, Rangers. Nathan Oduwa replaces Kenny Miller.
Substitution, Queen of the South. Jake Pickard replaces Mark Millar.
Substitution, Queen of the South. Kyle Hutton replaces Kyle Jacobs.
Rangers were much too slick for Queen of the South as they won comfortably at Palmerston Park in the Championship.