NEW YORK -- Facing three separate one-goal deficits against the undefeated San Jose Sharks, the New York Islanders showed resiliency and a third-period burst that made the difference Saturday night.

Right winger Kyle Okposo had a goal and two assists, and goaltender Jaroslav Halak made 22 saves in his season debut as New York surged past San Jose 6-3 at Barclays Center.

The teams entered the third period 3-3. Okposo, right winger Brock Nelson and center Frans Nielsen broke open the game against the Sharks, who appeared to sag in their second game in two nights.

"We know that they played a game last night so in the third period, we wanted to take the game over," Okposo said. "After (his) goal, we did a really good job of not giving them anything. We kept our foot on the gas and kept pressing."

The Islanders (3-1-1) outshot the Sharks 12-7 in the third period.

"It's a game we didn't finish," San Jose center Joe Pavelski said.

In the early going, it was the Sharks (4-1-0) taking the game to the Islanders.

Pavelski sent San Jose to the first intermission with a 1-0 lead. He deflected a point shot by defenseman Justin Braun before making contact with Halak. New York coach Jack Capuano challenged the call, but officials ruled the bump legal.

Islanders defenseman Johnny Boychuk and Sharks left winger Nikolay Goldobin scored 20 seconds apart in the opening minute of the second period. Left winger Anders Lee pulled New York back into a 2-2 tie when he banked a puck off the pads of goaltender Alex Stalock, who was in the process of removing his mask because a strap broke.

The officials discussed the goal, which was allowed to stand.

"Okposo took that one-timer up high and buckles came undone," Stalock said. "I just tried getting it off because I can't see when it falls on me. The ruling is when there's a scoring chance, they let it go. He let it go, and it ended up going off me and in."

Then San Jose right winger Joel Ward and Islanders left winger Josh Bailey exchanged goals to send the teams into the locker room tied 3-3 after two.

That set the stage for Okposo's wraparound goal at 4:18 of the third period and Nelson's insurance goal with 8:50 remaining.

It was the third straight game New York used a strong final 20 minutes at home to secure a victory.

"I thought we were able to grind them down," said Islanders center John Tavares, who along with teammate Ryan Strome had two assists. "We took the game over in the third period. It was a good win and good way to finish off this week."

Halak missed New York's first four games with an upper-body injury but didn't have to do much to earn his first win of the season.

"He played really well," Lee said. "It's always tough, your first game of the season, but he came in and played really well for us."

"It's good to be back. It's good to have this one under my belt," Halak said. "I'll take the win, although it wasn't pretty at times."

The Islanders have won three straight after losing their first two games of the season. They have the weekend off before facing winless Columbus on Tuesday, so a four-game winning streak could be on the horizon.

"We believe in ourselves in any position or any situation," Tavares said of the Islanders rallying three times Saturday. "There's no doubt in this locker room. We expect to win. Every game doesn't always go the way you script it. You don't always get the lead and we found a way."

NOTES: While G Jaroslav Halak made his season debut, G Thomas Greiss wasn't dressed as a backup despite starting three of the Islanders' first four games. Instead, G Jean-Francois Berube was on the bench. ... D Brian Strait and RW Steve Bernier were also scratched by the Islanders. ... Islanders C Frans Nielsen has 100 goals and 300 points in his career. ... The Sharks played their second game without C Logan Couture, who is expected to miss 4-to-6 weeks with a fractured fibula. ... D Paul Martin did not play because of a lower-body injury. He had played in all four Sharks games this season.