The Clyde players showed little signs of a hangover from their cup drubbing by Celtic as they weathered an early Queen's storm and then made tracks for goal.
In the first real attack it was only a tremendous save by keeper Richie Barnard at point-blank range from Ian Harty that prevented them making a break through.
But the opening goal came on 23 minutes following a corner from Clyde's right.
John Potter headed goalwards and though Steve Bowey stopped it on the line, the ball fell to Gary Bollan who slammed it home from close range.
Queen's replied by forcing four corners in succession, but found their way blocked by a rock-like Clyde defence.
Just after the interval Clyde had a penalty claim turned down when Harty seemed to go down on the edge of the box, but all it resulted in was a confrontation between him and Jim Thomson and both were booked.
Queen's put in a late rally, but the Clyde defence was resolute and keeper Bryn Halliwell had little to deal with.
In the dying seconds Eric Paton did get in a shot which flew just wide of the post.