Varlamov was 0-1-2 in his past three starts in his return to the NHL this season after having each of his knees partially replaced. The 38-year-old played two games at the end of last season with Bridgeport of the American Hockey League. He won both, allowing a total of three goals (.939 save percentage).
Brayden Schenn scored his 300th NHL goal, and Anthony Duclair and Bo Horvat also scored for the Islanders (6-4-2), who are 2-1-1 in their past four games.
Kyle Palmieri and Horvat scored in the shootout for New York.
Filip Forsberg had a goal and an assist, and Juuse Saros made 25 saves for the Predators (4-3-5), who have lost three of their past four (1-1-2).
Duclair gave the Islanders a 1-0 lead at 3:07 of the first period with the teams skating 4-on-4 when he tipped in a centering pass from Jean-Gabriel Pageau.
Schenn made it 2-0 at 8:07. Duclair sent a pass to the slot, and the puck deflected off Predators forward Nicolas Hague’s stick to Ondrej Palat, who fed Schenn for a backhanded tap-in.
Horvat extended the lead to 3-0 at 1:08 of the second period, one-timing Matthew Schaefer's cross-ice feed from the right face-off circle.
The Predators made it 3-1 when Forsberg buried a no-look pass from Jonathan Marchessault at the near post for a power-play goal at 9:42.
Alexander Kerfoot trimmed Nashville’s deficit to 3-2 at 13:02 by poking in a puck that trickled behind Varlmaov in the crease following a shot from Nils Hoglander.
O’Reilly tied it 3-3 at 4:16 of the third period, backhanding a rebound that Varlmaov was unable to locate off a shot from Daemon Hunt. The assist was Hunt's first point since being claimed off waivers from the Minnesota Wild on Saturday.
