Duffie converted a cross from Stewart Murdoch in the ninth minute of a combative tie played in freezing conditions at the Ochilview Stadium.
The visitors looked livelier throughout and created the majority of chances, but their build-up play was not matched by their finishing.
Jay Fulton twice headed wide from good positions, while Callum Reidford reacted well to deny Duffie a second goal.
Stenhousemuir improved before the interval, but two decent efforts from Sean Dickson were both repelled by Bairns goalkeeper Michael McGovern.
Conor McGrandles forced another smart save from Reidford after the break, and Greg Ross blazed wide from the edge of the area.
Reidford got down well to smother Thomas Grant's snapshot, and Lyle Taylor was off target in the closing stages as Falkirk held on.