Dubinsky skated toward the net from the left corner and flicked a shot at Capitals goalie Michal Neuvirth. The puck bounced high off Neuvirth and came down in the net behind him, enabling the Rangers to claim a victory in their Eastern Conference quarterfinal series after absorbing two road losses.
Erik Christensen and Vinny Prospal also scored for New York, and Henrik Lundqvist turned aside 23-of-25 shots for the eighth-seeded Rangers, who gained some momentum heading into Wednesday's Game 4 in New York.
Alex Ovechkin got his second playoff goal and Mike Knuble also found the net for the top-seeded Caps.
Neuvirth finished with 32 saves.