Billy Stark made a few changes from the side that lost to Stenhousemuir, John Weir & Jonny Whelan replaced the injured Richard Bowers & Stuart Kettlewell.
The first chance did not come until the twentieth minute. Paul Harvey's corner was flicked on by Tony Quinn and David Weatherston headered off the bar and over.
But, a couple of minutes later, Queen's took the lead. Mark Ferry broke through the defence before slotting the ball slowly past Derek Jackson with his left foot.
Queen's nearly doubled their lead on twenty five minutes. Derek Jackson fumbled a corner kick which let Paul Harvey attempt a lob from twenty yards cleared off the line at the back post by Jamie Mackay.
The Spiders did double their lead on the half-hour mark. Queen's won a free-kick on the half way line which was played over the top by Stephen Reilly and even though there was a hint of offside, David Weatherston managed to lob Derek Jackson for 2-0.
ex-spider Ally Graham headed over from six yards before Queen's got their third goal. Awarded a free-kick thirty yards from goal. Paul Harvey stepped up and curled the ball over the wall and into the net. A piece of genius from the experienced midfielder.
Though, early in the second half Shire pulled one back. A cross from the farside met the head of Ian Diack who headed past DC from three yards with a hint of offside.
Paul Tyrell came close with a header from Shire on 67 minutes but DC managed to tip it over the bar.
Queen's were starting to control the game again by now, and Steven Blair of the Shire, was sent off after two quickfire bookings for two poor challenges.
Queen's then seen out the game with no real problem with Jonny Whelan being replaced by Felvus.
Bring on the big boys in the second round.
QUEEN'S PARK: Crawford, Clark, Molloy, Reilly, Sinclair, Harvey, Weir, Quinn, Whelan (Felvus), Weatherston, Ferry
GOALSCORERS: Ferry, Weatherston, Harvey
BOOKINGS: Sinclair
REFEREE: Craig Thomson
ATTENDANCE: 234