In the extra session, Mattias Tedenby sent a pass from the neutral zone over to a streaking Salmela, who backed off his defender before snapping a wrister past Al Montoya for his first goal of the season.
Jacob Josefson and David Clarkson each had a goal and an assist for the Devils, who have won their past two games and six of seven, overall. Martin Brodeur faced just 15 shots in the game and stopped 13.
Blake Comeau and John Tavares each had a goal for the Islanders, who had won their previous two coming in. Montoya finished the game with 32 stops.
New Jersey got the only goal of the first period when the puck came out front from behind the net with an Isle and Devil tangled up and got past Montoya. Josefson got the credit for his first career goal at the 1:57 mark.
New York scored while shorthanded 73 seconds into the second. On the transition, Comeau attempted a pass, but the attempt was stopped. However, he was able to grab it and outlast Brodeur to the left side before flinging it home.
The Islanders then took a 2-1 lead at the 6:46 mark of the second as a left circle faceoff win saw Tavares deflect home a shot for his 25th goal of the season.
New Jersey tied the game 5:42 into the third as Clarkson jammed the puck home during a scrum in front.