Queens had to rely on a late winner from Mark Ferry after blowing numerous chances to bury the Fifers.
A loose clearance gave East Fife their best chance of the entire match after eight minutes, but John Boyle was denied a debut goal by the keeper.
After that it was all the Spiders, and Ross Clark was out of luck when his half-volley was touched over the bar after 17 minutes.
Billy Stark's men had a decent penalty shout when Paul Harvey beat the offside trap and teed up Brian Felvus, but he clashed with Craig Lumsden and hit the deck.
Queens continued to press, and Harvey smacked a drive just over the bar while Frank Carroll was off target with a free header.
East Fife's Scott Morrison pulled off an amazing point-blank save to keep out Alan Trouten's shot after 50 minutes, and Kevin Bain lunged in to clear the ball off the line.
The Fifers came close with a Graeme Mathie header after 56 minutes, but Queens threatened again when Felvus shot narrowly wide.
Referee Brian Winter waved away another penalty claim when Trouten fell in the box after a challenge from Bain.
Queens finally made the breakthrough with eight minutes left when Ferry collected the ball on the edge of the box and his shot found the bottom corner.
Steven Nicholas almost fired a late leveller for East Fife, but his shot whistled past the post.