The young Gers fought valiantly from an early two-goal deficit as Josh Gentles and Ashton Patton found the scoresheet once again, but it was the Doonhamers who prevailed through a Liam Smith hat-trick and Cole Coughlin strike.
From the team which overcame League Two leaders Clyde in midweek, in came Calum Young and Greig Thackray in place of Kyle Glasgow and Sam Reid.
The Doonhamers are unbeaten in this competition and they set their stall out early with a succession of opportunities through Connor Young, himself a former Rangers Academy player.
Smith was shimmying with intent on the right-hand side before laying on the forward before Young had a second bite of the cherry moments later when he swept goalwards from a pull-back but watched his effort cannon off Jack Wyllie.
On the scoresheet in midweek was Josh Gentles, who looked as sharp as he did in the victory over Clyde when he latched onto a loose ball on the halfway line and prompted an early caution for Shaun Want when he knocked the ball round the defender and looked to hare towards goal.
However, the Gers found themselves with an early uphill battle when the hosts struck twice in four minutes.
Too much time and space was afforded to Smith when he drifted in off the right and, despite the best efforts of Greig Thackray at full-stretch, arrowed an effort low into the bottom corner from the edge of the penalty area.
The away side were still licking their wounds from the concession of the opener when the winger struck once again, latching onto a pass before drifting his way through a succession of challenges inside the penalty area and rolling a smart finish beyond the goalkeeper.
Young flashed wide in an attempt to add a third three minutes later as the League One side certainly had Rangers on the ropes.
It prompted a reaction from the visitors as they pieced together their best move of the contest just shy of the half-hour mark.
Zander Hutton found himself in space advanced on the left, feeding Gentles before latching onto the forward’s return pass and forcing a smart save from Deniz Mehmet to his left.
With momentum on their side, Rangers hauled themselves back into the contest eight minutes before the interval.
His strike against Clyde four nights ago was something special, and again Gentles produced a moment of magic, this time from 30 yards out, when he turned, set his sights, and lasered a powerful effort which beat Mehmet for power and nestled spectacularly into the bottom corner.
Indeed, the Gers had the opportunity to restore parity just three minutes later when Zebedee Lawson pounced on a defensive lapse with only the goalkeeper to beat, but his dinked finish from a tight angle drifted agonisingly wide of the post.
Half-time saw a change in system for the Gers as Cameron Fernie’s introduction in place of Conor Owen facilitated a four-man backline.
Gentles showed tremendous persistence on the byline shortly after the restart after receiving a pass from Patton, and after Ben Hutton laid into the path of Luca Rankin the midfielder could only scoop an effort over the crossbar from the edge of the danger area.
Fernie tried his luck moments later after Rangers worked it well around the edge of the penalty box, but the midfielder’s effort sailed off target and was no trouble for Mehmet.
As the hour-mark struck, so too did a deserved leveller for the young Gers.
Patton had picked up exactly where he left off following his strike against Clyde, and his strike here was just as special as he jinked inside off the left – where he was moved at half-time – and curled a delicious low strike into the bottom corner and out of the reach of the Doonhamers goalkeeper.
From a free-kick, Lawson then had Mehmet scrambling with a rasping effort.
However, it was from the ensuing counter-attack that Queen of the South restored their advantage as they outnumbered the young Gers and Cole Coughlin finished low beyond Thackray at his near post after being teed up by Nicky Clark.
It was a bitter pill to swallow for the away side who had shown quality in abundance in the second period.
And just four minutes later, they were counting the cost of a fourth goal for the Dumfries outfit.
Smith once again showed his quality in and around the penalty area, benefitting from a fortuitous ricochet which brought the ball back into his path before he rounded Thackray and slotted home to seal the victory for the hosts.
RANGERS: Thackray, Young (Barr, 85), Kerr, Owen (Fernie, 45), Wyllie, Z. Hutton, Rankin (Owoyomi, 76), B. Hutton, Patton, Lawson, Gentles
Subs not used: Millarvie, Caldwell, Ramage, Reid, Wark, Molloy
QUEEN OF THE SOUTH: Mehmet, Charters, McQueen, Want, Rogerson, Davis, MacKenzie, Scott (Coughlin, 58), Smith, Clark (Ellis, 84), Young (Dair, 81)
Subs not used: Petry, Gray, Luissint, Kelly, McColm, Morton
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