Adam Edstrom gave New York a 2-1 lead 1:24 later with a high slot deflection of Lindgren's shot from the point at 10:24.
"They get one, then they get another, and you're behind on the road against a confident team," Philadelphia forward Garnet Hathaway said. "That's hard to come back from."
Miller made it even harder when he scored to make it 3-1 at 4:44 of the second period.
Artemi Panarin spun with the puck at the left-wing half-wall, moved up to the point and dished it across to Borgen, who quickly found Miller in the middle. He carried it to the top of the circles and scored with a blocker-side wrist shot through Vincent Trocheck screen on Ersson.
"We had some sustained O-zone pressure, broke down their defense and 'Borgs' made a great play finding me in the middle," Miller said. "I tried to make myself open and tried to get something on net."
Shesterkin made 17 saves in the second period. Tortorella said he counted 10 scoring chances in the period.
"I thought we developed a lot of offense," Tortorella said. "We couldn't solve their goalie."
Chytil extended the lead to 4-1 at 5:15 of the third period, scoring on a deflection of Vaakanainen's shot.
The Rangers outshot the Flyers 14-6 in the third after getting outshot 17-8 in the second.
"They were flying in the second period," Chytil said. "Luckily we scored one goal and we went two goals up. Then we scored the fourth one and it gives us more confidence in the third period."
Fox scored a short-handed empty-net goal at 16:53 to make it 5-1, and Smith added a power-play goal at 18:15 for the 6-1 final.
"Everybody in this room knew what we were capable of and how good of a team we are; I think it was just a matter of believing, honestly," Miller said. "These last couple games we've shown a lot of good things, how good of a team we can be when we're on. It's been great fun the last couple of weeks."
NOTES: This is the third straight season the Rangers have had a point streak of 10 or more games. It's also the 14th time in team history. … The Rangers lead the NHL with 43 goals in January. … Fox has 40 points for the sixth consecutive season. The only defensemen in Rangers history with as many consecutive 40-point seasons are James Patrick (seven from 1985-92) and Brian Leetch (six from 1993-99).