Queens made the perfect start to the match as David Weatherston fired them in front after only three minutes with a fine 25-yard strike. Elgin failed to deal with Mark Cairns' clearance and, as the ball bounced inside the Elgin half, Weatherston turned and struck a dipping volley over the helpless Kieron Renton.
Elgin were almost level five minutes later but Craig Campbell was unfortunate to see his speculative 25-yard effort come back off the woodwork with Cairns beaten.
But it was the Spiders that dominated the early proceedings and Elgin had keeper Renton to thank for stopping Billy Stark's men adding to their early goal.
Stuart Kettlewell made some good progress down the right before picking out Richard Bowers who was unmarked in the middle. But the youngster contrived to shoot weakly at the keeper when it appeared easier to score. Then, seconds later, it was Kettlewell's turn to spurn an excellent opportunity when he hit the side-netting from six yards.
Tony Quinn made sure of the points for Queens midway through the second half when he headed home from close range after Elgin failed to clear a free-kick.
Then Mark Ferry added the third ten minutes from the end with a low finish into the corner of the net after a fine passing move.