Islanders left wing Zach Parise, middle, celebrates with teammates after...

Islanders left wing Zach Parise, middle, celebrates with teammates after scoring against the Sharks during the third period of an NHL game in San Jose, Calif., Saturday. Credit: AP/Godofredo A. Vásquez

SAN JOSE, Calif. — It was a game the Islanders had to win as they faced the Western Conference’s worst team with a chance to get two victories on a three-game California swing.

And it was the gritty, methodical, heavy-hitting way the Islanders must play in their final 11 games.

“That’s the way we need to play down the stretch for sure,” Anders Lee said. “Bring that side of the game that we have and use it to our advantage.”

But mainly, Saturday night’s 4-1 win over the Sharks at SAP Center was necessary for their playoff push as they moved into the Eastern Conference’s first wild-card spot.

“It’s important regardless of the trip,” said Cal Clutterbuck, who was credited with a game-high seven hits. “The situation that we’re in, the amount of time and runway we have left, is more critical than the record on the trip. These games are all going to be approached with the same mentality, and that’s a must-win mentality.’’

The Islanders (36-27-8), who played with five defensemen the last two periods with Sebastian Aho absent from the bench, scored four unanswered goals. Ilya Sorokin, who started all three games on the trip, made 29 saves in his crispest California outing.

The Islanders lost to the Kings, 5-2, on Tuesday night but rebounded with a dominant 6-3 win over the Ducks on Wednesday night.

“It’s huge,” Jean-Gabriel Pageau said of going 2-1-0 on the trip. “You never want to drop the first one like we did. So I think we showed a lot of character. Two games that we needed and we got the job done.”

Pageau netted the shorthanded equalizer at 16:08 of the first period after being sprung by Casey Cizikas as he protected the puck from former Senators teammate Erik Karlsson and easily beat the defenseman to the crease. The Islanders already had failed to capitalize on three power-play chances.

“We came up dry on the power play early on,” coach Lane Lambert said. “To come out of that with a goal was a huge momentum swing. I think it was perhaps the turning point in the game.”

The Islanders got help from the Rangers, who beat the Penguins for the second time in three days at Madison Square Garden, 6-0. But the Islanders’ other metropolitan-area rival, the Devils, could not hold a two-goal lead entering the third period and lost to the Panthers, 4-2.

So the Islanders moved two points ahead of the Penguins, who have played two fewer games and now are in the second wild-card spot. The Panthers are three points behind the Islanders but also have played two fewer games.

“I’m not going to go out of my way to try and break down the mathematic equation that is probabilities and what’s left and that kind of stuff,” Kyle Palmieri said. “You pay attention to it and you’re aware of it, but at the end of the day, we want to be able to control our own destiny, and that’s what we’re looking to do.”

A dominant second period certainly helped.

Palmieri, coming off a career-high four points with a goal and three assists against the Ducks, tipped defenseman Scott Mayfield’s shot from the blue line to give the Islanders a 2-1 lead at 2:18. Defenseman Ryan Pulock’s power-play blast from the right point — the Islanders finished 1-for-5 on the man advantage with eight shots — pushed it to 3-1 at 5:25, with Pierre Engvall extending his point streak to four games with the secondary assist.

Kaapo Kahkonen stopped 29 shots for the Sharks (19-37-14), who are in an 0-4-2 skid and fell to 6-20-10 at home. They never were in the playoff race this season.

“Don’t look at their record,” Zach Parise said. “They play hard. They’re all over you on the ice. I thought it was physical both ways. And that’s always part of our identity, to finish checks on the forecheck.”

Kevin Labanc opened the scoring at 7:31 of the first period, just 14 seconds after the Islanders’ second power-play expired, as he used Aho to screen his shot from the slot.

Parise tipped defenseman Alexander Romanov’s shot to make it 4-1 at 5:19 of the third period.

Aho exited at 17:20 of the first period after taking a high hit from Labanc. Lambert said he had no immediate update after the game and that Aho will be re-evaluated on Sunday.

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