The Devils ended a four-game losing streak and gave themselves some room over Washington in the chase for the final playoff spots in the Eastern Conference. New Jersey moved past Ottawa into a tie with Philadelphia for the fifth best record in the conference. Washington is in ninth place and failed in a bid to climb over Winnipeg into a playoff position.
Parise's hat trick was the second of his career and lifted his goal total for the season to 27.
He opened the scoring on the power play 11:29 into the game, added a goal late in the first period and tallied again early in the second.
Hedberg has 20 shutouts in his 11-year career, the last two seasons having been spent with the Devils.
Michal Neuvirth stopped only 15-of-20 shots for the Capitals, who had won their previous four games.