New York's only point in its skid came in an overtime loss to Washington at home on Tuesday.
Rinne has posted all three of his shutouts this season in December, and the Predators have earned five blankings in 12 games.
It was the second straight game that Fiddler scored the only goal for the Predators. He gave Nashville the lead in the first period on a breakaway. Martin Erat, skating down the left side, hit Fiddler with a pass as he skated through the inside of the right circle. Fiddler fired a one-timer to beat Islanders goaltender Joey MacDonald to his glove side.
