Queens started the better side, but for all their early dominance they failed to put the Montrose goal under any serious pressure as Alan Trouten and Stuart Kettlewell both sent efforts over the bar.
Queens Park's best first half efforts came in injury time before the break. First Kettlewell saw a speculative overhead kick cleared off the line by Euan Hall. Then seconds later, Mark Ferry saw his 25-yard shot touched behind for a corner before the same player saw an effort blocked from four yards.
But Montrose broke the deadlock against the run of play with their first effort on target. Steven Kerrigan rose above the home defence to powerfully head home from 10 yards.
Queens were caught on the break as they pushed forward in search of an equaliser. Martyn Fotheringham was allowed to run unchallenged from the middle of the park before letting fly from 25 yards past Queens goalie David Crawford.
Fotheringham netted his second soon after, beating Crawford at his near post with a well placed free-kick from 20 yards.