Fisher scored his ninth goal at 18:12 of the first period off DiPietro, who was coming off consecutive shutouts against Columbus and the New York Rangers. His scoreless streak was stopped at 156:30.
DiPietro hadn't allowed a goal since Carolina's Scott Walker beat him early in the third period of the Islanders' 5-1 road loss to the Hurricanes a week ago.
"I can tell you honestly I don't really pay any attention to the shutout streak or anything like that," DiPietro said. "The biggest stat you can have is wins and that's all we were focused on tonight."
Kelly gave Ottawa an insurance goal at 16:29 of the third period when he redirected defenseman Anton Volchenkov's point shot past DiPietro with a second remaining in an Islanders bench penalty assessed against head coach Ted Nolan for abusing the officials.
Ottawa outshot New York 29-18 overall, including a 12-3 margin in the first.
"Overall it was just an effort from everybody, and when we have that, good things happen," Senators captain Daniel Alfredsson said. "They played yesterday and they didn't look like they forechecked very much today, and when they did, we were able to shut them down. We did a good job of having two or three guys back all the time."
The Senators won their second straight since losing leading scorer Jason Spezza to a knee injury in Thursday's 4-2 loss to Tampa Bay.
The Islanders, who beat the New York Rangers 2-0 Tuesday, suffered their first loss in the second of back-to-back games this season. New York had been 7-0 in that situation.
DiPietro caught a break to keep his shutout streak intact early in the first when Denis Hamel's slap shot from the right side struck the left post.
Fisher, who left late in the third with a lower body injury, gave Ottawa the lead 18:12 into the first as Ottawa finally got a puck past DiPietro, and on a fluky play, at that.
Fisher tapped home a loose puck in the crease after DiPietro was left stuck out of position when he moved across the crease from left to right as Alfredsson's pass to Dany Heatley deflected off Islanders defenseman Shawn Hill.
"If I had to play it again 10 times, I'd play it the same way 10 times," Hill said. "Sometimes you're going to get bounces that don't go your way, and it's all part of hockey."
Heatley had no sympathy for DiPietro's misfortune.
"I'm not going to feel for him. He made some plays on me later on," Heatley said. "He's a guy that reads and Alfie was coming to me and he would have been in a great spot for me, but sometimes that's the way it goes. It's a lucky bounce so we'll take it."
Emery stopped 10 shots in the second after facing only three in the first. He made another five saves in the third to complete his fifth career shutout as both teams managed just five shots apiece in a tightly played period.
"It's huge to learn how to play like that, to learn how to protect a lead like that and to get the results from playing a game like that," Emery said. "We played a pretty good game the other night against Tampa, kind of the same type of game but we let it slide late and we weren't rewarded for playing, for the most part, a pretty good game. So it was good to win one of those where we have a good defensive effort."
- Glenn Resch holds the Islanders' record shutout streak of 179:29 set during the 1975-76 season.
- As is customary at Scotiabank Place, Islanders captain Alexei Yashin was booed every time he handled the puck throughout the game. Yashin, who was traded by Ottawa to New York on June 21, 2001, remains the highest-scoring center in Senators' history. He had 218 goals, 273 assists and 491 points with Ottawa from 1993-2001.
- A Senators record crowd of 20,192 took in the game.