Clutterbuck scored the tiebreaking goal with 1:28 remaining in the third period, and the Islanders fended off the New York Rangers 6-4 on Sunday night.
Johnny Boychuk had two goals. Kyle Okposo had a goal and assist and Brock Nelson also scored for the Islanders and defenceman Nick Leddy had two assists. Frans Nielsen added an empty-netter with 1:01 remaining.
The Islanders, who led 3-0 and 4-2 before the Rangers rallied to tie it on Derick Brassard‘s goal with about 8 1/2 minutes to go, ended their season-high seven-game road trip at 6-1-0.
``It was a great play call by Zeeker,'' Clutterbuck said. ``I have to give him a lot of credit. He won the faceoff right on my tape. I caught it and flung it on net.''
Eric Staal had a goal and an assist for his first points with the Rangers in his fourth game since being acquired in a trade from Carolina just before the deadline.
It was the first meeting of the season between the rivals at Madison Square Garden and also a possible first-round playoff matchup next month. The Rangers are second in the Metropolitan Division with 82 points and the Islanders are third with 79, but the Islanders have three games in hand.
``We know we have games in hand, we know the situation,'' Okposo said. ``Obviously we're fighting for home ice down the stretch. We're fighting for a playoff spot.''
The Rangers have lost six of their past seven home games against the Islanders, going back to Feb. 14, 2013.
Raanta made 26 saves in his second consecutive start in goal in place of Henrik Lundqvist, who's day to day because of neck spasms suffered when he collided with teammate Ryan McDonagh in Thursday's loss to Pittsburgh.
Jaroslav Halak made 22 saves in his first start since Feb. 28 in a 3-1 loss against Edmonton. Halak is 3-0 against the Rangers this season.
Brassard's one-timer on the power play at 11:39 of the third tied it at 4-4 after the Rangers trailed 3-0 less than five minutes into the game. The goal was Brassard's team-leading 23rd of the season.
The Rangers, who are playing their third game in four days, got off to a slow start as the Islanders had several quality scoring chances early.
The Islanders took advantage and opened the scoring when Josh Bailey took a loose puck in the corner and passed to Boychuk, who beat Raanta with a wrist shot at 2:50.
Nelson converted a rebound of John Tavares' shot for a 2-0 lead at 3:35 and Okposo deflected Leddy's shot from the point on a power play at 4:45 to make it 3-0.
``(The) first period was the weirdest period of hockey in my life,'' Raanta said. ``It felt good early, got good saves, then suddenly five minutes off the clock and the game is 3-0.''
According to information provided by the Rangers from Elias, the Islanders scored three goals in the opening 4:45 of a game for the first time since Oct. 20, 2005, also against the Rangers.
``I'm not sure to be honest with you,'' Stepan said of the Rangers' slow start. ``Maybe the three (games) in four nights, but that's no excuse. I thought we really responded well after being down 3-0.''
The Rangers didn't get their first shot on goal until the midway point of the period, but then rallied with three goals in a 3 1/2-minute span.
Staal dug the puck out of the corner and passed to Lindberg, who slipped a backhand past Halak at 11:16. It was Lindberg's 12th goal of the season, but first since Jan. 9.
Only 38 seconds later, Dominic Moore's shot deflected off the back wall and Glass scored to cut it to 3-2.
The Islanders needed 80 seconds to score again when Boychuk's long shot from the right point got past Raanta for his second goal of the period and seventh of the season.
Staal capped a wild opening period when he banged home a rebound of Dan Boyle's long shot for his first goal with the Rangers at 13:45.
According to Elias, the previous time the Rangers and an opponent combined for seven goals in a period was April 19, 2013, at Buffalo.
NOTES: The Rangers and Islanders will finish their season series on April 7 at MSG. ... Rangers F Rick Nash missed his 19th consecutive game with a bone bruise in his leg and defenceman Marc Staal was scratched because of back spasms. Defenceman Dylan McIlrath left the game with a leg injury. ... Islanders D Calvin de Haan is day to day with a lower body injury. ... Jets defensive end Muhammad Wilkerson was in attendance.