Rolston faked Islanders goalie Al Montoya to the ice, then lifted a wrist shot over the prone goaltender into the net, handing the surging Devils their fourth consecutive win.
Rolston also scored in regulation and Ilya Kovalchuk added a marker for New Jersey, which kept its faint Eastern Conference playoff hopes alive with its 20th win in 24 games overall since Jan. 9.
Martin Brodeur made five saves in the tiebreaker and stopped 20-of-22 shots for the game in the Devils' win.
Blake Comeau forced an overtime when he scored an unassisted goal with less than 4 minutes remaining for the Islanders.
Josh Bailey also found the net and Montoya made 27 saves in New York's loss.