It was Sorokin’s first shutout of this season and 23rd in the NHL.
The Rangers are 0-6-1 at home and have been shut out five times, including twice in a row.
Jonathan Drouin and Jean-Gabriel Pageau each had a goal and two assists, and Anders Lee scored for the Islanders (7-6-2). Horvat has scored two goals in two of the past three games.
Igor Shesterkin made 21 saves for the Rangers (7-7-2), who have scored six goals in their seven home games, including five in a 6-5 overtime loss to the San Jose Sharks on Oct. 23.
Horvat gave the Islanders a 1-0 lead at 10:29 of the first period when he got behind Adam Fox and scored off the rush from the bottom of the left face-off circle.
Kyle Palmieri moved the puck up the ice on the right side to Emil Heineman, who entered the zone with possession and speed. Heineman found Horvat dashing past Fox and delivered a pass to the bottom of the left circle in stride so Horvat could put it in.
Drouin made it 2-0 at 19:27, finishing off a pass from Anthony Duclair as he drove the net following a Rangers’ neutral zone turnover.
Artemi Panarin couldn’t handle Mika Zibanejad’s pass along the wall and Pageau got to the puck. He moved it up to Duclair, who found Drouin in the middle. Drouin pulled off a forehand-backhand move and slid the puck past Shesterkin.
Horvat’s second of the game gave the Islanders a 3-0 lead on the power play at 18:42 of the second period.
Horvat, in the right circle, gave Drouin the puck down by the right post. Drouin had space and time but couldn’t find an opening, so he sent it back to Horvat with a backhand pass through Vladislav Gavrikov’s legs. Horvat sent a snap shot from the right face-off circle past Shesterkin’s glove.
Pageau scored into the empty net at 17:59 of the third period to make it 4-0, and then he led a 2-on-1 to set up Lee, who scored at 19:30 for the 5-0 final.