Annan could have equalised before half-time but Damiano Agostini did well to block Scott Anson's effort.
Nine minutes after the restart Peter Neilson lobbed his own keeper and Michael Moore tapped the ball in.
Stranraer: David Mitchell, Agostini, McInnes (Jones 82), Nicoll, Henderson, Wright, McGeouch, Danny Mitchell (Aitken 45), Moore, McColm (Jack 71), Noble. Subs Not Used: Montgomerie, Reid. Booked: Agostini. Goals: McColm 34, Moore 54.
Annan Athletic: Summersgill, Steven Sloan (Jack 62), McBeth, Watson, Neilson, Gilfillan, Jack Steele (Storey 62), Jardine, Cox (Bell 69), Anson, Lewis Sloan. Subs Not Used: Kelly, Inglis. Booked: Neilson.
Att: 358 Ref: J McKendrick
Source: BBC Sport
Source: BBC Sport