The visitors continued to promise much without hurting Clyde and the home side soon went ahead. A dreadful back-pass by Willie Gibson split central defenders Brian Reid and Jim Thomson and allowed former Queens player Alex Williams to shoot low past Richie Barnard.
Clyde continued to look the likelier side and an Eddie Malone cross was nodded down to Tom Brighton by Williams, but the shot was just wide.
More Clyde pressure forced Thomson to pull down Craig Bryson and Stephen O'Donnell's free-kick was brilliantly saved by Barnard.
Clyde then doubled their advantage when Bryson broke into the box, but although the defence blocked his run O'Donnell dispatched the loose ball into the net from the edge of the box.
The visitors replaced Derek Lyle by Brian McLaughlin at half-time which gave the side a better balance, and Malone cleared a dangerous situation for Clyde with a timely tackle in the six-yard area.
However, the early promise soon faded and Clyde went further ahead through a second Williams goal. Michael McGowan provided the cross and the striker powered a header behind the stranded Barnard.
Queens should have had a goal when McLaughlin released Tom English, but Gibson failed to reach the full-back's inviting cross in front of the unguarded Cherrie.
After that Clyde just coasted to the final whistle.