Dwayne Roloson was spectacular in goal for the Islanders, making a series of big stops among his 30 saves.
New York owned a 2-1 lead going into the third period, but Matt Hendricks scored to tie it midway through the frame.
Okposo then put a wrist shot past Craig Anderson to give the Islanders their second straight win.
Rob Schremp put the Islanders in front with the only goal of the second period. He reached up with his glove to knock the puck down from above his head and then took a full cut at it as if hitting a baseball. Schremp's stick caught the puck just right and it sailed under the crossbar for a bizarre goal.
Anderson made 32 saves in taking the loss.