Hedberg, playing in his 300th game, got the start as Martin Brodeur is expected to miss one to two weeks with a bruised elbow.
Dainius Zubrus also scored for the Devils, who won for only the second time at home (2-5-2).
The Capitals dropped their third straight, giving up 14 goals in that span.
Tedenby had a goal and an assist as the Devils jumped out to a 3-0 lead in the first period.
Elias got the opening tally on the power play at 5:49 of the first, deflecting Tedenby's shot with the shaft of his stick.
Arnott scored an easy wraparound goal at 16:15 as Capitals goalie Braden Holtby got tangled up Tyler Sloan, his own defenseman. Arnott circled behind the net to put the puck into the wide-open net before Holtby could recover.
Tedenby scored on a penalty shot with 1:46 remaining to close out the scoring in the period. After being fouled on a breakaway by Capitals defenseman John Erskine, Tedenby slipped a backhand past Holtby for his third goal in six games.
The three goals in the period equaled the Devils' total offensive output in the previous three games.
And New Jersey wasn't done.
In the second period, Arnott got his second of the game at 2:43, using his long reach to sweep a rebound past Holtby. Zubrus connected at 7:48 as the Devils extended the lead to 5-0.
Hedberg kept the shutout intact with a sparking glove save on Alexander Semin midway through.
Hedberg was sharp again in the third, stopping Alex Ovechkin on consecutive bang-bang screen shots from the right circle.
Notes: The Devils presented a video tribute and a moment of silence for Pat Burns before the game. Burns, who died on Friday after a long bout with cancer, coached the Devils to the 2003 Stanley Cup championship. The team will wear memorial "PB" patches for four straight home games. The jerseys will then be signed by the players and auctioned off with the proceeds going to a cancer hospice in Burns' memory. ÃƒÆ’Ã‚â€šÃƒâ€šÃ‚â€¦ Caps RW Mike Knuble missed a second straight game after taking a puck in the face. ÃƒÆ’Ã‚â€šÃƒâ€šÃ‚â€¦ The Devils recalled D Mark Frayne from Albany (AHL) on Monday. ÃƒÆ’Ã‚â€šÃƒâ€šÃ‚â€¦ Semyon Varlamov, recalled from Hershey (AHL) on Monday, was the Capitals' backup goalie.