Zibanejad put the Rangers ahead 4-0 54 seconds into the second period, and he completed the hat trick with a one-timer from the high slot off a pass from Strome to make it 5-0 at 2:06. Elliott replaced Hart after the goal.
New York was 3-for-5 on the power play; Philadelphia was 2-for-3.
In the past five games, Zibanejad has scored 15 points (seven goals, eight assists), 12 of them in the two games against the Flyers. He scored 11 points (three goals, eight assists) in the first 27 games.
"I don't know if self-doubt is the right word, but definitely it was a struggle for me to get the puck into the net," he said. "But I tried to stick by the work and just trust myself that it's going to come."
K'Andre Miller scored on the Rangers' first shot against Elliott to make it 6-0 at 2:42.
Claude Giroux made it 6-1 at 3:46, and Hayes scored on the power play to make it 6-2 at 13:34.
Buchnevich scored shorthanded 33 seconds into the third period to make it 7-2.
Fox got his fifth assist on the goal, tying a Rangers record and becoming the second defenseman with five in one game (Brian Leetch, April 18, 1995, against Pittsburgh Penguins).
"A lot of plays that look like they're going to be dead plays, doesn't have a play, and that's where a player makes a safe play, chips it out or whatever it might be, but it doesn't seem that's the case with him," Rangers acting coach Kris Knoblauch said. "He's always able to make that next play. Some guys can do it occasionally; 'Foxy,' it seems he can do it all the time."
Couturier scored a power-play goal at 1:28 to make it 7-3.
Filip Chytil made it 8-3 at 18:02.
"We're going to get an opportunity tomorrow to have our first practice in 12 days and we're going to get back to work," Flyers coach Alain Vigneault said.
NOTES: Zibanejad is the third NHL player to score six points against the same team in one season, joining Doug Bentley for the Chicago Black Hawks against the Rangers in 1942-43 and Joe Malone for the Quebec Athletic Club against the Toronto St. Patricks in 1919-20. He also is the third player in NHL history with two natural hat tricks against the same opponent in one season (Thomas Vanek for the Buffalo Sabres against the Tampa Bay Lightning, 2007-08; Peter Bondra for the Washington Capitals against the New York Islanders, 1995-96). ... Strome extended his point streak to seven games (two goals, 10 assists), and Fox extended his point and assist streaks to five games (one goal, 10 assists). ... Hart has allowed at least three goals in 15 of 20 starts, including seven straight, after he allowed at least three goals 15 times in 40 starts last season.