Alan Trouten went close to given the home side the lead in the sixth minute, but his 20-yard strike was deflected behind for a corner kick.
Queens keeper David Crawford did well to deny Craig Smart on the half-hour mark. Stuart Noble laid the ball off to Smart, but his effort was well blocked by the Queens goalie.
The home side had the bulk of possession and were unlucky not to break the deadlock minutes before the half-time break when Paul Paton hit the woodwork.
Tommy Murray sent in a dangerous cross from the right, but Paton's header came back off the left post with East Fife keeper John Dodd beaten.
Then seconds later, Queens Park hit the woodwork again. Alan Trouten's cross clipped the post and fell to teammate Stuart Kettlewell, who headed wide from close range.
Queens Park deservedly took the lead after 55 minutes when Tommy Murray coolly slotted the ball into the bottom corner from Mark Ferry's pass.
The goal spurred the visitors into action and they almost levelled after 63 minutes when Sean Paliczka saw his effort touched on to the post by David Crawford.
But the Spiders were two up 90 seconds later following an horrendous goalkeeping mistake by John Dodds. The keeper was deceived by a Trouten effort from the edge of the area and the ball stuck the goalie's leg before looping into the back of the net.