Defenseman Erik Gustafsson and center Claude Giroux also had goals for the Flyers, who will need to become the first team to win two in a row in this series to advance to a Conference Semi-final showdown against the Pittsburgh Penguins.
Rangers left winger Carl Hagelin ended Mason's shutout bid with 6:34 left in the game and center Mats Zuccarello scored a consolation goal in the final minute.
Game Seven of the Eastern Conference series will be played at Madison Square Garden on Wednesday, where the Rangers are 2-1 on home ice this postseason.
Mason, who did not start the first three games of the series because of an upper-body injury, was outstanding for the second time in three games.
He outplayed Rangers goalie Henrik Lundqvist, an eight-time All-Star and former Vezina Trophy winner, who allowed four goals on 23 shots and was replaced by Cam Talbot at the start of the third period.
Right winger Simmonds scored three of the first four goals of the game as Philadelphia raced to a 4-0 lead.
The longtime rivals meet in a Game Seven for only the second time in their history.
The Flyers beat the Rangers 4-3 in the deciding game of the NHL Semi-finals on May 5, 1974. Philadelphia then went on to defeat Boston for its first Stanley Cup title.
- Sports & Recreation
- Ice Hockey
- Pittsburgh Penguins
- Mats Zuccarello
- Claude Giroux