Rinne made 19 of his stops in the second period to protect the Predators' early advantage and it wasn't until there was just 3.58 left in the game before the Islanders got on the scoreboard with a deflection goal by John Tavares.
Nashville's goals came from Sergei Kostitsyn, Matt Halischuk and David Legwand.
Kevin Poulin made 29 saves in his second start of the season for the Islanders.
It was the Predators season-best, fifth-straight win and 14th in their last 18 overall. New York has lost four of six.