Richards scored less than two minutes in, and Del Zotto doubled the lead in the third period to help the top-seeded Rangers improve to 5-0 in Game 7s at Madison Square Garden.
That set up a matchup with the New Jersey Devils, the team the Rangers beat in the 1994 conference finals en route to their first Stanley Cup title in 54 years.
That series will open Monday in New York.
New York and Washington alternated wins and losses from Game 1 on, and this one didn’t come easy for the Rangers, who missed a chance to eliminate the Capitals in Game 6 on the road.
Just 38 seconds after Del Zotto made it 2-0 at 10:05 of the third, Roman Hamrlik sent a shot off of New York forward Derek Stepan that fluttered past Lundqvist for his only blemish of the night.
Braden Holtby played well in his second career Game 7, making 29 saves.
It was yet another heartbreaker for the Capitals, who were looking to reach the conference finals for the third time.
Six of Washington’s seven playoff losses were by one goal, and only one of its 14 games overall were decided by more than one.