A Greig McDonald double de-railed Stennies's title charge after the league leaders missed several chances.
The Warriors nearly scored in the first minute, but Iain Diack's shot was saved. The Fife defence then appealed in vain for offside, but John Dodds was quick off his line to block Jim Mercer's effort after eight minutes.
Paul Hampshire sent a wicked free-kick bending just wide after 24 minutes with William McCulloch rooted to the spot.
The league leaders wrestled the match back, and Dodds had to save from John-Paul McBride's free-kick.
McCulloch was caught cold after 46 minutes when he got underneath Kevin Gordon's cross, and McDonald headed in from close range.
Dodds was immediately called into action again as Colin Cramb tried to force a quick-fire leveller. But the Fifers were well on top, and Joe Savage was unlucky when he lobbed a stranded William McCulloch but the ball came back off the bar.
McDonald headed his second in the 53rd minute after a defensive nightmare as McCulloch again failed to gather a crossed ball.
Gary Kelly threw the visitors a lifeline after 74 minutes when he brought down Paul McGrillen and McBride converted the penalty. Substitute Craig Smart then missed two great chances to seal the win, but fortunately for the Fifers it didn't matter.