Montrose were first to threaten after eight minutes when a Martin Wood cross was headed down by Kevin Webster and Calum Watson had a close-range effort blocked.
A minute later Stephen Fraser put Craig Smart through but keeper David Crawford dived to save.
Queens Park had a chance in the 14th minute but Frank Carroll saw his close-range effort saved by James Butter.
After 26 minutes Shaun Molloy dribbled his way to the edge of the Montrose box and sent a thudding effort just wide.
Five minutes later a great turn by Watson gave him a shooting chance but Crawford was able to parry.
After 40 minutes Wood sent in a free-kick and Neil Stephen headed wide on the near post.
Three minutes from half-time a quick break by Montrose ended with Watson having a shot saved.
Montrose opened the scoring after 50 minutes when Wood beat two men on the left and fired home a low shot.
The home side made it 2-0 nine minutes later when Kerr Dodds was brought down by Gavin Rushford and Smart scored from the spot.
Queens Park pressed in a bid to get back into the game and after 76 minutes Butter had to turn away an effort from Carroll for a corner.
Right on full-time Queens Park were denied a consolation when a fierce shot from Bryan Felvus was tipped over by Butter.