Stranraer's Kevin Nicoll received two bookings and the Spiders' Ian Watt also saw red for serious foul play.
With the game set to finish a draw Malcolm nodded Lee Sharp's cross into the net to claim all three points.
Stranraer: David Mitchell, Gallagher, Bouadji (Daniel Mitchell 33), Nicoll, Sharp, Winter, Agnew, Murphy, Malcolm, Moore (One 41), McColm (Glen Mitchell 70). Subs Not Used: Marshall, McAuliffe.
Sent Off: Nicoll (75). Booked: Sharp, Nicoll.
Goals: Malcolm 90.
Queens Park: Strain, Little, Brough, Gallagher, Meggatt, Watt, Capuano, Anderson, Murray, Daly (Harkins 74), Eagleshan (Longworth 58). Subs Not Used: McPherson, O'Hara, McBride.
Sent Off: Watt (89). Booked: Anderson.
Att: 408
Ref: S Nicholls
Source: BBC Sport
Source: BBC Sport