Cuylle put the Rangers in front 2-1 at 10:14 with a wrist shot from the left circle after a stretch pass from Ryan Lindgren.
Horvat tied it 2-2 at 13:55, knocking in Nelson’s pass during a netfront battle with Rangers center Barclay Goodrow.
“He was lethal tonight. When he had a chance, you thought it was going in,” Islanders forward Mathew Barzal said of Horvat. “I thought he played a really solid game. I wish my line, some other lines, could have given him some help.”
The Rangers quickly regained the lead at 15:01 when Brodzinski redirected Miller’s one-timer to make it 3-2. Brodzinski was alone in front after Islanders defenseman Sebastian Aho got tangled with the Rangers forward while the latter was cutting to the net.
“It was a good breakout by us,” Brodzinski said. “Kicked it to the middle, (Alexander) Wennberg made a good drive wide and I just stopped at the net. “[Their] defenseman just fell in the corner. Wide-open in the slot, Miller just fired it into me, and just a small deflection.”
Kakko gave the Rangers a 4-2 lead at 2:36 of the third period. He won a puck battle against Islanders forward Pierre Engvall along the wall, skated into the right circle and sent a wrist shot past Sorokin for his 10th goal of the season.
Lafreniere one-timed Artemi Panarin’s feed at 10:42 for the 5-2 final.