Saints boss Derek McInnes signed a two-year extension this morning and three goals in six second-half minutes at McDiarmid Park - two by substitutes - ensured his side would be in the draw for the quarter-finals.
Jody Morris drilled in a 68th-minute penalty, substitute Marcus Haber tucked in a second goal four minutes later and fellow replacement Chris Millar added a third after 74 minutes as the Doonhamers were downed and Saints progressed to the last eight.
St Johnstone, who claimed their first Clydesdale Bank Premier League win of the season against St Mirren last Saturday, struggled to assert themselves in the first half against Irn-Bru First Division side Queens.
The 2008 Scottish Cup finalists from Dumfries brought five former Saints players with them to Perth and applied early pressure.
Paul Burns beat Danny Grainger in the opening minute and from the subsequent corner Saints cleared after goalkeeper Peter Enckelman fumbled.
Morris put Jennison Myrie-Williams through on the right at the other end and the winger cut back for Collin Samuel, whose near-post effort was blocked by Craig Reid.
The visitors' right-flank combination of Burns and Allan Johnston provided a threat, but it was Saints who had the better chances.
Liam Craig fired over after Lee Robinson had spilled Myrie-Williams' cross after 20 minutes before the Queens goalkeeper collected cleanly as Michael Duberry could not get much power on a header from a long throw.
Sam Parkin headed over from Grainger's cross before Johnston curled off target on the counter-attack following a strong run by Willie McLaren.
Samuel headed narrowly over from Maybury's cross after 35 minutes in the closest Saints came to scoring in the first period.
Craig was replaced at half-time by Millar, with Myrie-Williams switching to the left wing.
Myrie-Williams' distribution was poor, but he hit the post with a header after a deep cross from Millar and then had a stroke of good fortune when his cross struck the arm of Reid, with the defender positioned inside the box.
Referee Alan Muir pointed to the spot and Morris drilled the resulting penalty low into the bottom right corner.
Their confidence boosted, Saints pressed on.
Haber, a replacement for Samuel, latched on to Maybury's ball down the right, raced beyond the visiting defence and tucked in beneath Robinson for a second.
A third came when Parkin neatly flicked on Duberry's through-ball with his heel and Millar ghosted through before replicating Huber's near-post finish.
McLaren had an effort ruled out for offside in the closest Queens came to a consolation as Saints progressed.