The Islanders have played their best hockey of the season over the last couple of weeks. They might have gotten their best win of the season on Saturday night.

That came by dint of stopping the Kings from setting an NHL-record road winning streak of 12 straight games, which the Islanders did by beating Los Angeles by a 3-2 score in overtime courtesy of Jean-Gabriel Pageau’s game-winner — and flipping the season-long script to stage a third-period comeback of their own.

“I think we earned that win absolutely tonight,” Anders Lee said after scoring a pair of goals in the third period to send the game to OT. “Just the way we played for the whole game.”

On a night where the Islanders were bogged down in the neutral zone for the first two periods, the spark finally came via the combination of Lee and Mat Barzal with 11:18 to go in regulation.

Barzal got to a loose puck in the neutral zone and quickly shot it, with Lee right there to clean up the rebound.

Then with 4:11 to go, there was another rebound and there was Lee again, cleaning up Scott Mayfield’s initial shot from the point to tie the game at two.

“We knew,” Barzal said, “if we got one, we were going to get two. That’s pretty much all we were saying [during the second intermission]. There wasn’t a quiet moment, there wasn’t a down moment where we thought we were out of the game. We knew the game was right there.”

Cam Talbot and Ilya Sorokin traded great saves toward the end of regulation, with Talbot stopping a Kyle Palmieri rebound and Sorokin stoning Adrian Kempe on a breakaway.

But it was the Islanders’ resiliency that paid off just 13 seconds into overtime, as Simon Holmstrom sprung Pageau, who promptly buried the puck into the net.

“[Holmstrom’s] got great hockey IQ. I’ve said it for a while now, I think he’s making me better when I play with him,” Pageau said. “He makes the players on his line better. He makes a hell of a read, good chip, makes a hard play at a key moment in the game.”

In victory, the Islanders won their fourth game in five and collected their eighth and ninth points out of the last 10 available.

They also happened to do so against a club that entered Saturday with the best points percentage in the Western Conference.

Maybe Lane Lambert had a point when he kept saying he thought there were good signs afoot during the team’s seven-game losing streak in early November.

“We won’t get carried away here, but certainly in order for us to have the kind of success we want to have — we’re having success — we have to play a good 60 minutes,” Lambert said. “It’s certainly a step in the right direction.”

For the early part of the night, though, it looked like the offensive fuse that has lit the Islanders since then had gone out.

The Kings had seized control of the game after 25:12 of scoreless hockey when Scott Mayfield took exception to Andreas Englund’s legal hit on Barzal and fought the Kings’ defenseman.

Mayfield was given an additional two-minute unsportsmanlike conduct penalty in addition to both players getting five-minute fighting majors and the L.A. power play went right to work.

After just 28 seconds,Kempe rocketed in a one-timer off Kevin Fiala’s feed to the right circle.

Just a few minutes later, Vladislav Gavrikov would double the lead, beating Ilya Sorokin from the top of the left circle through Trevor Moore’s screen — which Lambert unsuccessfully challenged for goaltender interference.

Later on, though, the coach would describe his team’s mental state after 40 minutes by saying, “We felt like we were going to win the hockey game.”

Why?

“Because we had been playing well. Staying out of the penalty box, we’d give ourselves a chance. Thought we did that in the third period.”

For so much of the year, the Islanders have entered the last 20 minutes waiting for the other shoe to drop. On Saturday, they had nothing but belief in themselves.

“That’s something you guys don’t see in intermission,” Barzal said. “Just knowing the game was right there for us. I think this is a team that’s got good character. We’ve got a little bit of everything.”