Rolston collected a loose puck just to the left of Jhonas Enroth, moved to his backhand and slid it past the Sabres goalie, breaking a 1-1 tie 9:23 into the final frame.
Al Montoya turned aside 30-of-31 shots, including 14-of-15 in the third period for the Islanders, who beat Buffalo for the fifth time in six meetings.
Matt Moulson netted a power play goal for New York.
Jochen Hecht scored and Enroth finished with 28 saves for the Sabres.
Celebrity Families of 2014 [PHOTOS]