John Tavares and Anders Lee put the Islanders two up in the first period, before Colin Wilson halved their lead with two seconds of the period remaining.
Nick Leddy restored the Islanders’ two-goal advantage in the ninth minute of the third period, but the Predators were level after two goals in 30 seconds from Mike Ribeiro and Craig Smith.
Brock Nelson scored the go-ahead goal for the Islanders to ensure they replaced city rivals the New York Rangers at the Metropolitan Division summit.
Stanley Cup holders the Los Angeles Kings equalised in the closing stages of regulation time and then earned a 4-3 shootout victory against Eastern Conference leaders the Montreal Canadiens.
The Kings were sitting pretty after first-period goals from Marian Gaborik and Jeff Carter gave them a 2-0 lead, but they found themselves 3-2 down when Tom Gilbert, Brendan Gallagher and Max Pacioretty hit back for the Canadiens.
Marian Gaborik drew the Kings level with 45 seconds left and Anze Kopitar scored in the fourth round of the shootout to seal the points for the Kings.
The Arizona Coyotes’ long wait for a win is now at an end after they beat the Vancouver Canucks 3-2 to halt a 10-game losing streak.
Sam Gagner scored the only goal of the shootout after neither side could claim victory in regulation time.
The Tampa Bay Lightning moved to within two points of the Canadiens at the top of the Atlantic Division standings by recording a 4-2 victory against the Toronto Maple Leafs.
Nikita Kucherov scored his 24th goal of the season, while Ryan Callahan, Vladislav Namestnikov and Alex Killorn were also on target for the Lightning.
David Schlemko celebrated his Calgary debut by scoring the winning goal in the shootout as the Flames defeated the Boston Bruins 4-3.
Third-period goals from Michael Del Zotto, Wayne Simmonds and Michael Raffl gave the Philadelphia Flyers a 3-1 triumph over the St Louis Blues.
The Minnesota Wild also left it late to overcome the Washington Capitals, with a final-period brace from Jason Pominville securing a 2-1 win.
Dallas goaltender Jhonas Enroth stopped all three Florida shootout attempts and Colton Sceviour scored the third-round winner to help the Stars edge past the Panthers 4-3.