Dubielewicz stopped Michael Nylander, Brendan Shanahan and Jaromir Jagr in the shootout. The save on Jagr's shot was the best. Dubielewicz made a diving save as the puck just fell short of the goal-line.
Miroslav Satan had the only shootout goal. He beat Henrik Lundqvist with a backhand in close in the first round.
Arron Asham and Satan scored for the Islanders, who won the eight-game season series from their rivals 5-3.
The Islanders needed a win because Montreal and Toronto both won. They are four points behind the Canadiens and three behind the Maple Leafs, with a game in hand on both.
Shanahan and Nylander scored for the Rangers in regulation. The Rangers would have clinched a playoff spot with a win, and wound up falling into seventh place as Tampa Bay won. Both teams have 92 points, but the Lightning have more victories (44 to 41).
Lundqvist stopped 32 shots.