The Gers finally appeared to have run out of legs in the last 10 days of the season, losing the UEFA Cup final to Zenit St Petersburg and then the Clydesdale Bank Premier League title to Celtic on Thursday night.
In contrast, this was Queens' first game since finishing fourth in the Irn-Bru First Division 28 days ago.
Kris Boyd was the Hampden hero again with the opening goal, before DaMarcus Beasley put his injury hell firmly behind him with one of his own.
Yet brave Queen of the South fought back and spectacularly cancelled out the deficit in a three-minute spell after the interval by Steve Tosh and captain Jim Thomson.
However, with just under 20 minutes of a gripping contest remaining, Boyd was the Rangers saviour with his 25th goal of the campaign as he met a Beasley corner to nod the winner.