Opening the scoring for the Warriors was Iain Diack, who was making his debut after leaving the 'Shire when Dennis Newall was sacked. The goal after 28 minutes was a close-range strike from a Jim Mercer knock-down.
This was about the only action from a woeful first half in which Stenhousemuir rarely stepped out of first gear.
The Shire almost equalised five minutes after the resumption when Willie McCulloch pushed a Derek Ure rocket round the post.
Any hopes of a comeback were ended after 58 minutes when Paul McGrillen beat his marker and surged into the box, and with no fewer than three Stenhousemuir players lining up to tap the ball home he spotted a gap and drilled the ball into the net.
Four minutes later he scored his second when he headed home a Tommy Sinclair cross from close range.
Karl Lejman almost scored at the other end after 78 minutes, but his shot was tipped on to the bar by McCulloch.
A minute later McGrillen scored his hat-trick when he headed home a rebound from a Stevie Fallon shot, and with three minutes left David Templeton made it 5-0 when he passed the ball past the advancing Derek Jackson.