Kyle Okposo, Sundstrom and Justin Johnson gave the Islanders a 3-0 lead after the first period. Sundstrom added his second goal in the middle period and John Tavares scored in the third for the Islanders.
"With our 5-on-5 and special teams play, we've accomplished what we wanted to accomplish," Islanders coach Jack Capuano said. "We've still got Tuesday, Wednesday and Thursday of next week to work more on those things. All of our guys have battled for the last few weeks. Unfortunately, you can only keep so many of them."
New York is off until it opens the regular season on the road Friday night against the New Jersey Devils.
Robin Lehner stopped 33 shots for the Senator, who begin a season-opening six-game trip with a visit to the Buffalo Sabres on Friday night.
"This is a hard League and if you don't come prepared to play and work any team in this League can beat you," Senators coach Paul MacLean said. "That team that played us flat outworked us in every area of the game and deserved to win and that should give us a real good wake-up call going into next week."
Material from wire services was used in this report.