Stranraer broke the deadlock in the 25th minute after a series of amazing escapes for Queens, with the ball cleared off the goal-line three times by defenders, before Allan Jenkins managed to squeeze the ball home close in at the post.
But Queens were level three minutes later when David McNiven dummied a pass from Eric Paton and the ball ran through to John O'Neill, who warded off a challenge and slipped the ball beyond the keeper.
The game fell a bit flat after the break but picked up again midway through the half, with Queens unlucky when McNiven cracked in a 25-yard shot which beat the keeper but hit the bar and Paul Burns headed the rebound over.
Queens keeper Colin Scott was lucky to escape with a yellow card when he came out of his box and tried to head clear but handled.
Jenkins later had the ball in the net following a free-kick, but his effort was ruled offside.