Steve Reilly's last-minute penalty killed off the Fifers' play-off hopes as they dropped eight points behind Queens.
East Fife fans staged a protest against chairman Derek Brown before the match, and their mood didn't improve when their side failed to have a serious effort on goal for 44 minutes.
It was a must-win game for Jim Moffat's men, who were five points and a place behind the Spiders who were in the last play-off spot.
But it was Queens who threatened, and Bryan Felvus was unlucky after 26 minutes when his quicksilver shot cannoned up off the keeper's legs and hit the bar.
East Fife's only effort in a dire first half was a Joe Savage header which drifted past the post from Paul Hampshire's free-kick.
On the stroke of half-time East Fife keeper John Dodds had to be brave when he dived at Felvus' feet to stop the striker's run on goal.
In the second half Savage robbed dithering Reilly after 65 minutes, but his cut-back was wasted by John Bradford.
Queens Park should have buried the Fifers in the 71st minute when David Weatherston raced to the line and pulled the ball back for Mark Ferry, but his shot lacked the power to beat Dodds.
Veteran Paul Harvey then picked the lock of East Fife's defence, but the keeper blocked Kevin Proctor's close-range drive.
With just a minute left East Fife's Elliott Smith send Ross Clark tumbling in the box, and Reilly coolly sent the keeper the wrong way.