The midfielder smashed home a penalty after 31 minutes following a handball from Marvin Andrews.
David Weatherston's right-footed effort from six yards out after 72 minutes gave Queens hope, but Morton held out despite Kevin Finlayson being sent off.
Queen of the South: Hutton, Reid, Harris, Andrews, Lilley, Burns, McKenna, Quinn, McLaren (Weatherston 46), Holmes, Knight (Kean 46). Subs Not Used: Fox, Scally, Hamill.
Booked: Quinn, Reid, McKenna, Lilley.
Goals: Weatherston 72.
Morton: Stewart, McGuffie, Reid, Shimmin, Greacen, Finlayson, Jenkins, Masterton, McAlister, Weatherson (Graham 88), Russell (McKinlay 80). Subs Not Used: Cuthbert, MacGregor, Tidser.
Sent Off: Finlayson (77). Booked: Masterton, Finlayson, Graham.
Goals: Masterton 7, 31 pen.
Att: 2,611
Ref: C Brown
Source: BBC Sport
Source: BBC Sport