Barclay Goodrow scored for the Sharks (14-28-6), who have lost five of their past six games (1-5-0). Alexandar Georgiev made 27 saves.
“We just can’t make these boneheaded mistakes that end up in the back of our net,” Sharks coach Ryan Warsofsky said. “And we get away from them as who we are as players and as a team. And, until we do that, we’re going to be seeing the same result.”
Barzal gave the Islanders a 1-0 lead at 8:47 of the first when he slid a backhand past Georgiev’s right pad on the breakaway.
Goodrow tied it 1-1 at 10:02 with a wrist shot from the top of the right face-off circle that deflected off Islanders defenseman Alexander Romanov’s stick and over Hogberg’s blocker.
Nelson put the Islanders ahead 2-1 just 40 seconds later. Kyle Palmieri chipped the puck to Nelson in the low slot and he beat Georgiev over the glove from the top of the crease.
“I just hopped out there and tried to get on the backcheck,” Sharks forward Will Smith said. “But it was kind of a choppy little pass, and it ended up going in.”