It was the first preseason game for each team.
K'Andre Miller scored a shorthanded goal, and Brennan Othmann had two assists for the Rangers. Dylan Garand made nine saves in relief of Shesterkin, who played 31:41 after winning the Vezina Trophy last season voted as the best goalie in the NHL.
Robin Salo scored for the Islanders, who lost in Lane Lambert's first game as coach. Semyon Varlamov allowed four goals on 20 shots in 31:15 before being replaced by Jakub Skarek, who made 15 saves.
Jimmy Vesey gave the Rangers a 1-0 lead on the power play at 10:51 of the first period with a sharp-angled shot over Varlamov's left shoulder from the right side. The 29-year-old forward, who played his first three NHL seasons (2016-19) with the Rangers, is in training camp on a professional tryout contract.
Chris Kreider made it 2-0 on a rebound at 15:48.
Miller extended the lead to 3-0 with four seconds left in the period when scored off a feed from Othmann, who chased down a loose puck in the corner after an Islanders turnover.
Zac Jones pushed it to 4-0 with a one-timer at 11:41 of the second period.
Salo scored at 16:10 for the 4-1 final.
