The Rangers are off to the second round of the playoffs on the power of a four-game series sweep.
The Blueshirts beat Washington 4-2 in Game 4 on Sunday.
Artemi Panarin scored the winner at 16:39 of the third period to break a 2-2 tie at Capital One Arena.
Kaapo Kakko, Vincent Trocheck and Jack Roslovic had the other Rangers’ goals.
The Blueshirts advance to play the winner of the Islanders-Hurricanes series.