"We knew how important this game was and we came in here and had a strong game," said Crosby, who scored for the first time in nine games.
It was the second shutout of the season for Jarry, who made 34 saves in a 4-0 win at the Buffalo Sabres on Dec. 1.
"It always helps to get those," Jarry said. "There was a couple [of shutouts] where I might have left one on the table, I let one in late so it was nice to get that."
The Islanders have lost five straight games in regulation for the first time since Nov. 19-29, 2013.
"We had a good first period," New York forward Cal Clutterbuck said. "It was 0-0 and then just making mistakes that you can't make as a professional. It's 1-0, they get a power play and it's 2-0 and we're chasing the game again. It's been the storyline a lot lately."