Schaefer scored his 14th goal, the second-most in NHL history by an 18-year-old defenseman behind Phil Housley, who had 17 goals before his 19th birthday in 1982-83. Schaefer was previously tied for second with Bobby Orr, who scored 13 goals as an 18-year-old in 1966-67.
In addition, Schaefer's goal was his fourth game-winner this season, moving him past Denis Potvin for the most by a rookie defenseman in team history.
He also tied Vladimir Malakhov (1992-93) for the second-most goals in a season by an Islanders rookie defenseman behind Potvin (17 in 1973-74).
Carson Soucy scored against his former team and Ilya Sorokin made 20 saves for the Islanders (30-19-5), who defeated the Rangers 5-2 at UBS Arena on Wednesday, 5-0 at Madison Square Garden on Nov. 8 and 2-0 at home on Dec. 27.
It's the first time since 2017-18 that the Islanders have swept the regular-season series against the Rangers.
Mika Zibanejad scored and Jonathan Quick made 19 saves for the Rangers (22-27-6). New York played its second game without Artemi Panarin, who is being scratched for roster management purposes because he is expected to be traded.
Soucy scored at 17:18 of the second period to give the Islanders a 1-0 lead.
Max Shabanov got the puck across the zone to Soucy in the left circle close. He snapped a shot that snuck through Quick and into the net on the short side.
The Islanders acquired Soucy from the Rangers on Monday.
Schaefer extended the lead to 2-0 just 1:35 later, scoring from the top of the left face-off circle with a short-side shot that went over Quick's pad and under his blocker with Simon Holmstrom providing a screen in front of the goalie at 18:53.
Zibanejad cut it to 2-1 at 2:48 of the third period with a power-play goal on a one-timer from the left circle.
