Patrick Kane answered that goal to tie it at 2 at 6:08 of the third, but Erik Christensen put New York back on top just 28 seconds later.
Dubinsky, who leads New York with seven goals, got the Rangers even 1-1 in the final minute of the first period. Both goals were set up by linemates Ryan Callahan and Artem Anisimov.
Henrik Lundqvist made 33 saves as the Rangers won their second in a row and earned just their second home victory (2-3-1).
FLYERS 3, HURRICANES 2
In Philadelphia, Scott Hartnell scored two goals and Claude Giroux added one to lead Philadelphia.
Playing without center Danny Briere, who began a three-game suspension for a crosscheck on the Islanders' Frans Nielson on Saturday, the Flyers won their fourth in a row after losing four of five and took over sole possession of first place in the Atlantic Division. The Hurricanes have lost two of three.