Islanders goaltender Rick DiPietro saw his shutout streak stopped at 156 minutes 30 seconds on Fisher's first-period goal and Kelly added a power-play goal late and the Senators (19-18-1) held on to win for the second game in a row. The shutout was the second of the season and fifth of his career for Emery.
The victory, before a sellout crowd of 20,192 at Scotiabank Place - the most ever to watch a hockey game at the building, was just Ottawa's seventh of the season on home ice in 16 outings.
DiPietro finished with 27 saves for the Islanders (19-14-3), who had their two-game win streak stopped.
The Senators have dominated the Islanders over the years. Since Feb. 12, 1996, Ottawa has lost just four of 40 regular-season games between the teams, going 28-4-8-0 over that span.
Alexei Yashin, still a target of boos from Senators fans every time he touched the puck, failed to record a point for the first time in six games.
DiPietro came into the game having posted back-to-back shutouts, including a 2-0 victory over the New York Rangers one night earlier, and had held the opposition goal-less in three of the Islanders' past four games.
The Senators outshot the Islanders 12-3 in the opening period and DiPietro's shutout streak came to an end when Alfredsson tried to set up Dany Heatley in the slot only for his pass to deflect off of a sliding Sean Hill and wind up on Fisher's stick at the side of the net for an easy tap-in with less than two minutes to play in the first.
Emery faced more pressure in the second and third periods and needed a toe save to prevent a goal off a deflection by Shawn Bates.
With 7½ minutes remaining in regulation, New York self-destructed when Richard Park and Alexei Yashin took tripping and hooking minors, respectively, on the same play and the Islanders' bench received a third penalty for unsportsmanlike conduct after the initial calls.
The Islanders had one second left to kill when Kelly scored on a redirection with 3:31 to play.
Ottawa went 1-for-5 on the power play; New York was 0-for-1.
Notes: Senators centre Jason Spezza missed his second game in a row with a knee injury. . . . Islanders defenceman Freddy Meyer missed his sixth straight game with a lower-back injury. He hasn't played since being acquired from Philadelphia on Dec. 16. . . . Ottawa plays host to the Rangers on Friday. . . . The Islanders are at New Jersey on Saturday.