Nelson scored in the fifth round, as the Islanders (21-18-4) snapped a five-game losing streak heading into their "bye week."
Miles Wood and Taylor Hall scored 37 seconds apart early in the third period to give the Devils a 4-2 lead, but the Islanders forced overtime on goals by Sebastian Aho (7:58) and Cal Clutterbuck (15:43).
Anders Lee and Anthony Beauvillier also scored for the Islanders, who are off until Saturday. Jaroslav Halak made 42 saves in regulation and overtime before stopping all five shots he faced in the shootout.
Travis Zajac scored twice for the Devils (22-11-8), who have lost five straight (0-2-3) heading into their bye week. New Jersey is also off until Saturday. Goalie Cory Schneider made 34 saves in regulation and overtime before stopping the first four shots he faced in the shootout.
Lee scored the only goal of the first period when he backhanded home a rebound of a shot by Ryan Pulock with 4:32 left.
Zajac's own backhanded rebound of a shot by Sami Vatanen tied the game 4:43 into the second. Beauvillier put the Islanders ahead following a Devils turnover deep in the New Jersey zone with 9:16 left, but Zajac tied the score again with a semi-breakaway shorthanded goal with 4:35 remaining.
A pair of turnovers by Islanders defenseman Nick Leddy led to the two early third-period goals by the Devils. New Jersey center Pavel Zacha poked the puck free from Leddy behind the New York net to set up Wood's go-ahead goal, which he scored after backhanding home a rebound of a Will Butcher shot.
Moments later, Leddy was preparing to receive a pass near center ice when his stick broke. Wood picked up the loose puck to begin a sequence that ended with Hall beating Halak.
--Field Level Media
New Jersey | NY Islanders | |
Travis Zajac 2 | Points | Sebastian Aho 2 |
Travis Zajac 2 | Goals | Sebastian Aho 1 |
Taylor Hall 1 | Assists | Mathew Barzal 2 |
N/A | Power Play Goals | Sebastian Aho 1 |
Travis Zajac 1 | Short Handed Goals | N/A |
Cory Schneider .895 | Save Percentage | Jaroslav Halak .913 |
Cory Schneider 34 | Saves | Jaroslav Halak 42 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
New Jersey | 46 | 4 | 0-5 | 2-3 | 6 | 31 |
NY Islanders | 38 | 5 | 1-3 | 5-5 | 10 | 37 |