Callahan, who had nine previous two-goal games and two four-points outbursts in the NHL, scored twice in the first period when New York built a 2-0 lead, added another in the second when the edge grew to 4-0, and netted his 20th of the season in the third with a goal off his skate.
New York got top-line forward Marian Gaborik back in the lineup for the first time in seven games following a concussion. He didn't get on the score sheet, and it didn't matter. Mats Zuccarello added two goals and Artem Anisimov also scored for the Rangers, who snapped a four-game losing streak at home while wearing their road whites at Madison Square Garden for the first time this season.
Callahan, who added an assist in the third period, has 10 goals and six assists in 16 games since returning from a broken hand on Feb. 1.
Henrik Lundqvist was sharp, making 24 saves in his NHL-leading ninth shutout, but he didn't need to be to shut down the sluggish Flyers, who have dropped a season worst four in a row and are in danger of losing their hold on first place in the Eastern Conference.
New York, seventh in the East, leads eighth-place Carolina by three points and ninth-place Buffalo by four.
The Rangers were back home for the first time since being swept on a three-game homestand in which they were outscored 8-4. The Garden skid began two weeks earlier when the Flyers beat New York for the fourth time in four meetings this season.
New York has won two in a row overall, including a thorough 4-1 win at Ottawa on Friday.
The Flyers, however, are heading in the opposite direction following their most lopsided loss this season.
Since taking a 2-0 lead at home through one period of a 5-3 loss to Buffalo on Saturday, Philadelphia has been outscored 12-1. Brian Boucher stopped only 14 of 18 shots before being pulled 6:28 into the second period when Callahan finished his hat trick with an unassisted goal. Sergei Bobrovsky, who allowed four goals on 34 shots in Saturday's loss, came on in relief.
Callahan got the Rangers going 51 seconds in with a redirection of a pass from Brandon Dubinsky, and made it 2-0 with 7:02 left in the first with a power-play goal.
Zuccarello pushed the lead to 3-0 at 5:06 of the second, and Callahan then chased the shaky Boucher. He struck again 4:20 into the third against Bobrovsky, turning his left skate to steer the puck into the net. Anisimov made it 6-0 with 5:19 left off an assist from Callahan, and Zuccarello netted his second with 1:13 remaining.
Notes: It was the Rangers' second four-goal game of the season. Gaborik did it against Toronto on Jan. 19. ... Zuccarello has a goal in consecutive games after going 18 without one. ... The Flyers didn't have any penalties in their previous visit to MSG on Feb. 20, but racked up 32 minutes on nine calls in this one. They were 0 for 5 on the power play, making them 3 for 35 in the past 10 games. ... New York's Sean Avery had a goal disallowed 1:46 into the second when video replay showed he kicked the puck into the net. ... Bobrovsky allowed three goals on 18 shots.