Emil Heineman and Anthony Duclair also scored, and Logan Stanley had two assists for the Islanders (2-2-0). Ilya Sorokin made 22 saves.
Frank Nazar scored, and Arvid Soderblom made 15 saves for the Blackhawks (1-4-0).
Horvat gave New York a 1-0 lead on the power play at 19:03 of the first period. He won a face-off back to Matthew Schaefer, whose wrist shot from the point was stopped by Soderblom before Horvat gathered the rebound in front, pushed the puck to his left and scored inside the left post.
Sorokin stopped a Cole Smith backhand on a breakaway at 1:08 of the second period. The goalie slid into the net on the play, but after a video review by The Situation Room, there was no conclusive evidence to determine whether the puck crossed the goal line.
Heineman beat Soderblom from the high slot to give the Islanders a 2-0 lead at 6:44 of the second. Matias Maccelli found him cutting into the slot with a pass from the right wall.
Duclair pushed the lead to 3-0 at 9:38, burying a one-time pass by Logan Stanley from the right side.
Nazar ended Sorokin's shutout, cutting it to 3-1 at 17:26 of the third period with Soderblom pulled for the extra attacker. He beat Sorokin high blocker side with a one-timer from between the circles off a pass from Patrick Kane.
Horvat then scored into an empty net for his second of the game and the 4-1 final at 18:27.
