Marcus Hogberg made 25 saves in his second straight start for the Islanders (17-19-7), who had their three-game winning streak end.
New York was shut out for the sixth time this season.
“I’m going to give them some credit, they did a good job boxing us out,” Islanders coach Patrick Roy said. “But, I mean, we didn't go to the net enough. We didn't generate enough offense by throwing pucks at the net. Maybe we tried to be a little too perfect.”
Gaudette thought he scored the opening goal for Ottawa at 1:42 of the first period, but New York challenged the play for goaltender interference, and the call was reversed after a video review.
Gaudette did, however, make it 1-0 at 8:42 of the second period by redirecting Kleven's point shot over Hogberg’s blocker from the top of the crease.
“It felt good for sure,” said Gaudette, who ended a 15-game goal drought. “Everybody gets cold streaks. That's the way it is, in the game and in life. So, what you got to do is just keep your head down, keep working and eventually it'll go in.”