Jason Arnott, Brian Rolston and Patrik Elias also scored for the Devils (2-0-3). Martin Brodeur stopped 23 shots.
"There's an upbeat tempo to our game," Brodeur said. "We have skill. I think we have the firepower to play a certain way, compared to past years, that's for sure."
Matt Moulson scored twice, Jesse Joensuu had one and Dwayne Roloson made 24 saves for the Islanders (0-3-0).
Parise's slap shot from the slot with 5:46 left in the first gave the Devils a 2-1 lead.
Rolston and Elias scored even-strength goals 4½ minutes apart in the second period to push the Devils' lead to 4-1.
"We played well, made some mistakes, but we got the win and that's the most important thing," Devils coach John MacLean said.
Moulson scored at 14:28 of the second period to pull the Islanders to 4-2, and his second goal closed the scoring at 11:18 of the third.
"I hope I score two goals every game," said Moulson, who had a career-high 30 goals last season. "I think I have a lot to prove. I want to score goals and I want to win."
Joensuu beat Brodeur with a backhander for the game's first goal at 1:38 of the first period. Arnott tied the score 3:17 later, tipping in a shot by Andy Greene past Roloson.
Islanders stars John Tavares and Rick DiPietro sat out but are expected to play Saturday when the teams conclude their preseason schedules at Nassau Coliseum.