The other three quarter-final ties in the competition were played over the weekend, with each of them settled in the regulation 90 minutes.
First Division pacesetters Thistle were comfortable 3-0 winners over Raith at Firhill but they had to wait until the second half to break the deadlock.
After Chris Erskine opened the scoring, Steven Craig made it two and Erskine rounded off a decent day’s work with the clincher just eight minutes after his first strike.
Cowdenbeath were made to work hard for their 2-1 victory at East Stirlingshire after Marc McKenzie’s goal was cancelled out by Sean Kelly.
Kenny Adamson eventually settled the tie for the Blue Brazil with the decisive goal five minutes before the break at Ochilview.
Arbroath progressed thanks to a narrow 1-0 triumph against their fellow Second Division side Stenhousemuir, with Scott Robertson’s first-half counter making the difference.
If Gers can see off Queens in their repeat of the 2008 Scottish Cup final eight days from now, it will guarantee a new name will be inscribed on the Challenge Cup trophy this season.
But the Doonhamers, winners in 2002/03 against Brechin at Broadwood, will be determined to ensure their bid for a second title goes on.
You can still get tickets for that game now by calling 0871 702 1972, visiting Rangers Ticket Centre or visiting the ticketing section of the club website.
Seats cost £15 for adults, £10 for concessions and £5 for children, with a £2 discount per category for season ticket holders.
Tickets for each match will be available right up to kick off if they remain available but fans are advised to purchase them early to avoid queues and disappointment.