In a game that had three distinct periods and as many twists and turns as possible in the long-running Rangers-Islanders rivalry, it took one play late in the third period to resurrect the Islanders in their 6-4 win Sunday at Madison Square Garden.

The Rangers came all the way back from a 3-0 deficit established in the first 4:45 of the game, with Derick Brassard’s power-play goal tying it at 4-4 at 11:39 of the third period.

The turning point came when Derek Stepan lost a critical defensive-zone faceoff to Casey Cizikas, who slid the puck behind him to Cal Clutterbuck. His wrister from the top of the left circle nipped goaltender Antti Raanta’s right shoulder and hit the top corner with 1:28 left for a 5-4 lead.

“It’s a tough loss,” Stepan said. “We get the game even and I kind of choked for us, and that’s no good. If you’re the guy that’s relied on to make that play, you’ve got to be better. In Washington [a 3-2 win Friday night], I’m out there for the last one and I win it back. Tonight I lose it.”

Raanta, who called the first-period onslaught — goals by Johnny Boychuk, Brock Nelson and Kyle Okposo in a 1:55 span — “the coldest nightmare,” said he “took one step to the middle and it opened up the side and [Clutterbuck] got his shot straight through to the top shelf. After the first period [which ended 4-3 Islanders], you don’t think anything can go worse than that.”

The Islanders (36-20-7, 79 points) pulled within three points of the Rangers (38-22-6, 82) — who are in second place in the Metropolitan Division — and have three games in hand. It was the Islanders’ third win in three tries against the Rangers this season. The teams will meet at the Garden on April 7.

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Eric Staal, who had his first points in his fourth game as a Ranger since arriving from Carolina — a goal and assist — said he didn’t think the Rangers were “engaged mentally, both execution and battle level. We weren’t crisp.”

“It was a strange first, just one of those things,” Clutterbuck said. “The puck was bouncing everywhere, for both teams. You usually need divine intervention for that many goals in a period in the NHL these days. It just doesn’t happen.”

The last time that happened when the Rangers were involved was on April 19, 2013, when the Rangers and Sabres totaled seven goals in the second period of an 8-4 Rangers win in Buffalo.

The Rangers didn’t have a shot until Staal’s slap shot at 10:50, but he then stopped Boychuk’s attempted clear and found Oscar Lindberg for a short-side backhander, his first goal in 23 games, at 11:16. The Rangers scored again 38 seconds later as Dom Moore’s slap shot slammed off the end boards and caromed to the left post, where Tanner Glass put it home, and the Garden was alive again. Boychuk’s second, on a long shot, restored the two-goal lead at 13:14, but Staal scored 31 seconds later to make it 4-3.

Neither team scored in the second as the goalies settled in, and after Clutterbuck’s goal, Frans Nielsen’s empty-netter with 1:01 to play sealed it.

“We dominated the first period,” Islanders coach Jack Capuano said. “We were up 8-0 in shots, they didn’t have a sniff. Then we make a bad play around the boards and they get one. The [Rangers] are a good team, they played hard. But for me, it probably shouldn’t have even come down to that [late goal].”