The Greenock men went into the clash hoping to pile the pressure on second top Dundee United but they were well beaten in the end.
The Doonhamers carved out the first opportunity when Stephen Dobbie sent a left-foot shot narrowly wide from 20 yards.
Dom Thomas then tried his luck with an ambitious long-range effort which flew harmlessly wide.
At the other end Morton finally threatened when Lawrence Shankland’s header forced a smart save from Lee Robinson.
Queens responded with Derek Lyle and John Rankin both thwarted by Derek Gaston.
Gaston’s saves were matched by Robinson who produced two excellent efforts to deny Ricki Lamie and Shankland again.
The match turned decisively in Queens’ favour midway through the second half when Lyle met a Thomas cross with a firm header which finally beat Gaston.
Thomas O’Ware and Ross Forbes both went close to drawing Morton level before the Dumfries side went into over-drive to secure the points.
First Kyle Jacobs unleashed a shot from outside the box and watched in delight as the ball soared high into the net.
And that effort was matched in stoppage time by Joe Thomson whose 20-yard shot beat Gaston at the bottom corner.