Silfverberg, who assisted on the Senators' regulation goal, skated in on Brodeur in the shootout and fired a right-handed wrist shot that caught the NHL's all-time wins leader by surprise. When Bishop stopped former Senator Bobby Butler on the Devils' third shootout attempt, Ottawa (8-6-2) had its third road win of the season.
Ilya Kovalchuk and Patrik Elias were both stopped by Bishop in the shootout as the Devils (9-3-4) lost their second straight.
Stephen Gionta scored his second goal of the season in the opening minutes of the game, but the Devils were silenced the rest of the way by Bishop.
Daniel Alfredsson scored for Ottawa in the third period, tying the game at 1 with 11:48 remaining on his 420th career goal.
Brodeur made 29 saves for the Devils.
New Jersey entered overtime down a man, but managed to kill the power-play chance. Alfredsson had the lone shot on Brodeur during the power play, a shot Brodeur smothered, sending the game to the shootout.
The Devils controlled the action early on, collecting 17 shots in the first, their highest total for one period this season.
Just 1:19 into the game, Steve Bernier's wrist shot was stopped by Bishop, but Gionta alertly jumped all over the rebound for his second goal of the season when he slid the puck between Bishop's pads for a 1-0 lead.
The Senators had the better of play in the second period, as well as the scoring chances.
Eric Gryba's shot with 11:23 left in the second was initially stopped by Brodeur, but it trickled behind him and was pushed aside just before it reached the goal line.
With 10 minutes left, Silfverberg's slap shot clanked off the post as it went by Brodeur. Just 15 seconds later, Silfverberg's shot was stopped by Brodeur, but he didn't know where it was.
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The Devils went almost 10 minutes of the second period without a shot before Senators right wing Chris Neil was sent off for slashing. Marek Zidlicky's slap shot from the point was stopped by Bishop, but broke the shot drought. The Devils had only four shots on goal in the second.
The Devils had a good stint in the third period when Patrik Elias, Alexei Ponikorovsky and Ilya Kovalchuk had solid shots against Bishop, who started for only the third time this season.
The Senators' relentless pressure paid off when 40-year-old captain Alfredsson lifted a backhand over a diving Brodeur to tie the game. The 17-year veteran, who has four goals this season, is the Ottawa's all-time leading scorer with 1,090 points (420 goals, 670 assists).
It was the first time the Senators scored since they lost All-Star defenseman Erik Karlsson to a season-ending Achilles tendon injury last Friday.
NOTES: Devils D Mark Fayne, who had two giveaways that led to goals in New Jersey's 5-3 win over Philadelphia, was a healthy scratch for a second straight game. ... Devils rookie F Stefan Matteau was a healthy scratch for a third straight contest. ... The Devils recalled C Andrei Loktionov from Albany (AHL) and sent struggling C Jacob Josefson back to Albany. Josefson had only one assist in 15 games this season. ... When Loktionov was with the Los Angeles Kings, his roommate was Alexei Ponikorovsky, who was recently re-acquired by the Devils. ... The Devils lost LW Ryan Carter to an upper-body injury when he was sandwiched into the boards by Ottawa's Chris Neil and Dave Dziurzynski in the second period. Carter did not return. ... Devils RW Bobby Butler faced his former team for the first time. ... Senators LW Milan Michalek has a sprained knee and was a scratch for the third straight game. Michalek is joined on the Senators' injury list by All-Stars Jason Spezza (back) and defending Norris Trophy winner Erik Karlsson (Achilles tendon surgery).
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