Luciano Slagveer came close to opening the scoring with a rocket of a shot that just flew over the bar, before Thern grabbed his first after some poor De Graafschap defending allowed the midfielder to knock the ball into an empty net.
Mitchell te Vrede then got a debut goal after converting the ball in from close range.
Thern got his second goal of the evening, heading into the bottom corner, before Dean Koolhof hit the post for Graafschap as they tried to get back into the game.
Vincent Vermeij had a chance cleared off the line before the young striker gave Graafschap a consolation goal with a header into the top corner.
Heerenveen's next fixture will be an Eredivisie match away to FC Utrecht on August 16.