Roloson did not have to stop more than six shots in a period en route to his eighth career shutout and first since Nov. 21, 2001. He improved to 5-1-1 in his last seven starts.
Dupuis broke up the goaltending duel 6:30 into the middle period when his wrist shot from the top the slot appeared to change directions before beating Olaf Kolzig to the glove side.
It was the sixth goal of the season and first career game-winner for Dupuis.
Kolzig turned aside 30 shots, but the Capitals had trouble generating scoring chances and fell to 0-2-1 in their last three games.