Gregor Buchanan ended Morton’s winless streak with a killer header four minutes from time.
It looked like being another night of frustration for manager Jonatan Johansson who hadn’t enjoyed a win since 4 January against a stubborn Queens side who had defended so well.
However, after Robert Thomson’s shot was pushed wide by Alan Martin, Michael Tidser swept over the corner and Buchanan made it his to head home from close range.
Morton deserved it as they moved above Queens into sixth.
Twice Smith denied Reaghan Tumilty, making fine blocks in 15 minutes and then again just before half time.
Jordan Marshall made a sensational interception to deny Andy Dallas in 27 minutes and Barry Maguire threw himself in front of Reece Lyon’s shot to divert the ball wide for a Morton corner six minutes later.
Stephen Dobbie was always a threat as Queens tried to hit Morton on the counter. He forced a smart save out of Robby McCrorie in 42 minutes after a brilliant turn.
And the Morton keeper made good blocks in 53 minutes and 79 minutes.
However, Morton got the win they craved thanks to Buchanan’s late intervention.