Couture won it when he one-timed Evander Kane's feed in the right circle for his fifth goal of the season. Couture also scored in overtime in the Sharks' 2-1 win at the Vegas Golden Knights on Thursday.
The goal extended Couture's point streak Couture to six games (three goals, seven assists).
"Those are two plays where I'm just kind of in the right place at the right time," he said.
New York had one shot on goal through their first three power plays, and 10 over the next three. San Jose has the top penalty kill in the NHL (42-for-44, 95.9 percent).
"They're No. 1 in the League for a reason; they put a lot of heat on you," Trotz said. "They take away a lot of your options, they put you in small spaces and jump you, and you've got to make some plays. I thought we adjusted as the game went on. We kept adjusting in doing things and we were getting a little more zone time and some looks, but we didn't find the back of the net.
"But I liked the fact that we were skating, we were drawing penalties. Because we were skating, they had to haul us down. As I said, it comes down to a play."
Sorensen finished a 2-on-1 by redirecting Mario Ferraro's pass to give the Sharks a 1-0 lead at 6:38 of the second period.
"It was a great pass by Mario," Sorensen said.
The Islanders tied the game 27 seconds later when Casey Cizikas deflected Adam Pelech's shot to make it 1-1 at 7:05. DeBoer challenged for goalie interference, but the call stood.
"We didn't really give them much," Cizikas said. "A lot of their chances were getting point shots that got through, and they were just trying to get on the rebound. I thought our defense did a great job. We had opportunities, but we just couldn't cash them in on this case."
New York outshot San Jose 11-5 in the third period.
"I wish we had a couple more scores, but once you get to overtime, you know it's insane," Pelech said. "[It's] anybody's game, and we deserved a better result."
