The Hampden side were unlucky on ten minutes when Aidan Keena’s 35-yard drive came crashing back off the bar and their misfortune continued a minute later when Luke Donnelly’s shot beat Chris Smith only for Ross Meechan to stick out a leg to clear.
It got worse for the hosts on 17 minutes when Stenhousemuir took the lead when McGuigan turned a Ruardh Donaldson cross in using a combination of his head and shoulder.
The equaliser came four minutes from the break when Ross Millen’s low driven free-kick was met by the diving Gerry McLauchlan and his header squeezed over the line.
The hosts were forced into a change 17 minutes from time when Millen was knocked out by a clearance from McLauchlan.
The decisive strike in the tie came nine minutes from time when Harry Paton darted forward and released McGuigan with a fine through ball and the striker slid the ball into the corner.