The first leg will be at Somerset Park on Tuesday evening.
For the hosts, Mark Ridgers returned after a dislocated finger. Aaron Doran, Jamie McCart and Liam Polworth were rested on the bench ahead of the Premiership play-offs.
With only cash rewards and play-off scheduling at stake, it was a slow-burner, but Nathan Austin sliced a low shot wide after 15 minutes.
Ridgers made a strong save as on-loan Aberdeen striker Bruce Anderson turned neatly and struck.
The breakthrough came after a mistake from Pars debutant Stuart Morrison. The midfielder’s pass-back came too fast at keeper Cammy Gill, bouncing against his face.
That left Austin needing only to keep his composure and stroke a low shot past the flailing Gill.
The Pars almost struck back three minutes after the break, with a tremendous curling attempt from Kallum Higginbotham tipped wide of the post by Ridgers.
Substitute Andy Ryan also swept a shot just high and wide with 15 minutes remaining.
With five minutes left, Tom Walsh’s 12-yard strike was turned against the post by keeper Gill.