Defenseman Mark Fayne started the rush by poking the puck to Gionta at the blue line.
He made outstanding stops on Adam Henrique from the left circle and on a couple of chances in front by Stephen Gionta.
"We pride ourselves on being there every year, " forward Stephen Gionta said.
Gionta gave the Devils the lead at 13:55 of the first period, just a second after an effective Capitals power play expired.
Ryan Carter, Stephen Gionta and Dainius Zubrus also scored as New Jersey won its second in a row after a 10-game losing streak (0-6-4).
Devils D Bryce Salvador (lower body) and C Stephen Gionta (upper body), who were both hurt in Monday's 3-2 shootout loss to Ottawa, played.
Carter scored in close at 14:11 for a 4-2 lead, and he made a steal at the blue line to set up Gionta for a 5-2 lead.
Before being sandwiched by defenseman Tomas Kundratek and Troy Brouwer, the Swede swept the puck to Gionta, who beat Neuvirth one-on-one for his second career regular-season goal.
The two squared off after Martin checked Stephen Gionta and Martin caught the New Jersey tough guy right on the jaw with a right that sent him to the ice.
Brian Gionta's power-play goal at 6:07 of the third the 20, 000th goal for the Canadiens since the NHL was formed in 1917 had tied the game at 3.
After giving up a rebound goal to Stephen Gionta just 1 minute, 19 seconds into the game, Bishop was perfect, making 16 saves in the first period and fending off three shootout attempts.
WSJ: For Devils Against Bishop, Scoring Goals Turns Out to be a Tall Task
Stephen Gionta and Patrik Elias scored for the defending Eastern Conference champion Devils, who are off to their first 3-0 start since the 2002-03 season, the last time they won the Stanley Cup.
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