Jim McIntyre’s side ended a disappointing week with a good away win against another side with play-off aspirations.
The game took over half an hour to get going, but it came to life when Morton went close on 36 minutes, with Tony Wallace’s shot cleared off the line by Andy Dowie.
Morton seemed to be on the ascendancy, with Kabba Cham played in by Scott Taggart, but Dowie blocked his shot.
Then, a minute before the break, Michael Paton was the architect with a run and cross from the byeline for Iain Russell to head home.
Morton went close on the stroke of half-time with Michal Habai shooting narrowly wide.
On 50 minutes, Taggart sent over a pinpoint cross but Habai sent his right-footed volley over the bar.
Queens got their second on 58 minutes with a sweetly struck 22-yard shot from Derek Lyle after an Ian McShane pass.
Morton appeared to be thrown a lifeline just two minutes later when Russell was adjudged to have handled. However, Reece Hands fired the penalty over the bar at an important time and Queens then saw the game out comfortably.