Patrik Elias and Mattias Tedenby each contributed a goal and an assist and Hedberg notched his first shutout of the year in his 300th career game for the Devils, who broke a three-game losing streak.
Dainius Zubrus also chipped in with a tally for New Jersey.
The Capitals, meanwhile, dropped a third straight game for the first time this season and were beaten by a 5-0 margin for the second consecutive time.
Braden Holtby stopped only 18 of 23 shots in Washington's loss.
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