The win gave Ottawa a sweep of two home games and a 3-1 lead in the best-of-seven Eastern Conference semifinal series. Ottawa can advance to the conference final with win in Game 5 on Saturday night in New Jersey.
Dany Heatley and Daniel Alfredsson also scored for the Senators, who used some lapses by goaltender Martin Brodeur to take a 3-1 lead and hang on for the win.
Jay Pandolfo's first goal of the post-season at 9:36 of the third closed the gap to one goal. Brian Gionta scored in the second period for the Devils.
A Scotiabank Place record crowd of 20,248, most dressed in Senators' red, turned out to see the home side outskate New Jersey and outshoot them 36-31.
Fisher, used mainly as a checking centre in the post-season, darted across the New Jersey blue-line and fired a shot that beat Brodeur to the glove side 3:58 into the third period. Goalie Ray Emery got an assist on the goal.
Ottawa opened the scoring when Alfredsson took a drop pass from Jason Spezza, slipped the puck to Heatley behind the net and got open to one-time the return pass over Brodeur 4:34 into the game.
But the Senators took the first four penalties of the game and the Devils finally capitalized 4:17 into the second frame when Gionta followed in to bang in Patrick Elias' rebound.
It was Gionta's league-leading eighth goal of the playoffs and third of the series and Brodeur got an assist for starting the play. It also ended Ray Emery's home shutout string at 152 minutes 33 seconds.
Emery had shutouts in his last two home playoff starts - Game 5 of the first round against Pittsburgh and Game 3 against New Jersey on Monday. He last allowed a goal at home to the Penguin's Sidney Crosby at 11:44 of the third period on April 14
Brodeur continued to struggle with bad-angled shots from the right side as Heatley put Ottawa back in front at 14:44.
Heatley's surprise turn-around shot along the ice from a very tight angle found its way through sticks and skates and into Brodeur's net.
Vincent Lecavalier scored two similar goals, also from bad angles from the right side, in the opening round against Tampa Bay.
The Senators' only visit to the conference final was in 2003, when they lost in seven games to New Jersey.
Notes - Devils' fourth-liner Michael Rupp sat out for the first time in the playoffs and was replaced by Toronto native David Clarkson, who made his NHL playoff debut in Game 1 of the series but sat out the last two games... Ottawa and New Jersey are both playing in the post-season for a 10th straight year, tied for the second-longest current streak behind Detroit's 16.