Nelson gave the Islanders the win after they faced deficits of 3-0 and 5-2 by finishing off a breakaway from rookie Matthew Barzal.
Barzal finished off his third career five-point night by stealing the puck from Gustav Nyquist. Once Barzal gained possession, he made a saucer pass through the slot to Nelson, who simply lifted the puck over Detroit goaltender Petr Mrazek for the winner.
Nelson finished with his second career hat trick and scored twice in New York's five-goal third period.
Nelson also scored one of the four power-play goals the Islanders had in a span of 3:37 after Cal Clutterbuck drew a slashing penalty on Tyler Bertuzzi with 6:33 left. Bertuzzi hit the Islander forward on the left knee with his stick.
The Islanders set a team record for power-play goals in a period.
Anders Lee, Nick Leddy and Josh Bailey also scored on the power play after Detroit took a 5-2 lead on a power-play goal by Anthony Mantha 9:54 into the third.
Nelson and Lee started the comeback on the power play before Leddy made it a one-goal game with 3:21 left. Bailey gave New York its first lead at 6-5 by slapping John Tavares' cross-ice pass over Mrazek with 1:49 remaining.
The lead lasted 80 seconds, as Detroit defenseman Mike Green tied the game on a disputed goal. The Islanders contended Justin Abdelkader should have been called for goaltender interference, but the goal stood.
Jordan Eberle also scored for the Islanders while Tavares set up two power-play goals. Jaroslav Halak earned the win by making six saves after Thomas Greiss was pulled.
Henrik Zetterberg had a goal and three assists for Detroit. Darren Helm also scored in the third period for the Red Wings while Mantha and Martin Frk scored in the first period before Zetterberg ended a 15-game goal-scoring drought to give Detroit a 3-0 lead.
--Field Level Media
Detroit | NY Islanders | |
Henrik Zetterberg 4 | Points | Mathew Barzal 5 |
Anthony Mantha 2 | Goals | Brock Nelson 3 |
Henrik Zetterberg 3 | Assists | Mathew Barzal 5 |
Anthony Mantha 1 | Power Play Goals | Brock Nelson 1 |
N/A | Short Handed Goals | N/A |
Petr Mrazek .759 | Save Percentage | Jaroslav Halak .857 |
Petr Mrazek 22 | Saves | Thomas Greiss 27 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Detroit | 39 | 6 | 1-2 | 3-7 | 19 | 33 |
NY Islanders | 29 | 7 | 4-7 | 1-2 | 9 | 27 |