Spartans qualified for the Challenge Cup first round despite losing to Threave Rovers in the preliminary round second leg.
With , neither side created much in a tame first half.
Dean Fyfe fired the ball into the corner of the net to give Threave a lifeline.
But Spartans keeper Scott Bennett saved low show from Scott Wilby late on to preserve Spartans' lead.
Spartans progress to face holders Queen of the South on 27 July in the first round proper.