Cal Clutterbuck and Anders Lee each had a goal and an assist, and Semyon Varlamov made 23 saves for the Islanders.
Brennan Othmann, Barclay Goodrow, and Will Cuylle scored in the third period for the Rangers. Jonathan Quick allowed four goals on 25 shots before being replaced at the start of the third period by Dylan Garand, who saved all seven shots he faced.
Jean-Gabriel Pageau gave the Islanders a 1-0 lead at 7:07 of the first period.
Brock Nelson made it 2-0 at 9:37. Artemi Panarin turned the puck over to Hudson Fasching, who left the puck for Nelson with a between-the-legs pass.
Bo Horvat extended the lead to 3-0 at 17:11 on a wraparound, and Clutterbuck pushed it to 4-0 at 10:44 of the second period.
Othmann scored his second goal of the preseason to make it 4-1 at 5:07 of the third period.
Goodrow got the Rangers to within 4-2 at 16:22, and Cuylle cut it to 4-3 with 50 seconds remaining.
However, Lee scored an empty-net goal with eight seconds remaining for the 5-3 final.
