Robbie Ftorek scored on two power plays in Philadelphia and Ron Duguay got two goals as New York won its series, 3-1.
The Rangers, who won both games in Philadelphia, next meet the winner of the New York Islanders-Pittsburgh Penguins matchup in the Patrick Division final.
Ftorek scored the first goal at 9:37 of the opening period, skating in alone from the left wing and connecting on a backhand. He scored again at 3:42 of the second period on a tip-in of Reijo Ruotsalainen's shot from the blueline. That goal came 1:33 after Andre Dore fired in a slap shot from the left point.
Ftorek's second goal gave the Rangers a 3-0 lead and they upped their advantage to 6-2 on Dave Maloney's power-play shot at 1:25 of the last period. Then the Rangers had to hold off a furious onslaught by the Flyers.
A goal by Bobby Clarke, his second of the game, at 4:08, and goals by Darryl Sittler at 13:33 and by Bill Barber at 16:19 made it 6-5. But New York goalie Ed Mio, who faced 16 shots that period and 43 in the game, kept Philadelphia from tying and Duguay scored into an empty net with seven seconds remaining.