The Islanders had a decent push early in the second, but Bishop came up with a couple of big saves, stopping Jordan Eberle on a two-on-one. A short time later he got a glove on a point-blank chance by Jason Chimera and then got some help from Seguin who cleared the puck away as it rolled toward the goal line.
The Stars made it a 4-0 game at 6:54 of the second with a shorthanded goal. Islanders forward Josh Bailey threw the puck into the slot in his own zone, Janmark picked it off and ripped it past Halak.
"I thought the fourth goal was the big goal," Hitchcock said. "There was a surge going on, they were on a power play, and that fourth goal really took the wind out of them and the game."
Spezza's first goal of the season, which came from the left circle with the Stars on the power play, made it 5-0 at the 16:00 of the second.
"It's nice to score a goal and contribute offensively," Spezza said. "Obviously it's been a long time for me, hopefully it's something I can build off of."
The Stars limited the Islanders to just four shots in the third period as they wrapped up their three-game homestand with a 2-1-0 record.