Queens almost levelled after 23 minutes when Alan Trouten burst on to a loose ball just outside the area and drove a fierce shot just wide of Fife stopper John Dodds' near post.
The Spiders looked good after the break with both Michael Dunlop and Johnny Whelan going close during a period of good pressure which failed to yield the leveller.
The Fifers then passed up a great chance to tie things up after 65 minutes when front man Craig Smart smashed a penalty off the Queens Park post after Andy McGinty upended John Bradford in the area. Bradford himself almost took advantage of the re-bound, but could only screw his shot into the side netting.
The busy John Martin won a second penalty for the hosts after 87 minutes when he was brought down by Ritchie Sinclair, but the striker's joy was short lived as keeper David Crawford dived to save his firmly struck shot at his right-hand post.