Markus Naslund also scored for the Rangers, 8-1 in their last nine games at Madison Square Garden. Daniel Briere scored for the Flyers, and Martin Biron made 29 saves.
Callahan had a hand in both goals as the Rangers took a 2-0 lead in the first period.
New York scored 52 seconds in as the Rangers stormed the crease, chasing a loose puck. Naslund, who was credited with the goal, and Callahan took multiple swipes before the puck - and Biron - both slid into the net.
Referee Don VanMassenhoven pointed to the goal, signaling a score - a decision that was confirmed by a video review.
Callahan scored at 12:06, deflecting Derek Morris' blast from the right point.
Briere scored the only goal of the second period at 9:14. With Philadelphia on the power play, Briere flipped a shot over Lundqvist on what had effectively become a 5-on-3 advantage.
Rangers defenseman Paul Mara was severely hobbled after blocking a slap shot from Kimmo Timonen. Mara limped off the ice after the goal was scored but returned later in the period.
Early in the third, Lundqvist preserved the Rangers' one-goal lead with a spectacular diving glove stop on Daniel Carcillo.
The Flyers got a power play when Naslund was whistled for interference on Biron at 10:05. Philadelphia failed to capitalize but the Flyers did have a golden opportunity to even the score when Briere hit the crossbar with 4 minutes remaining.
Notes: Sean Avery and Nik Antropov were in the lineup for the Rangers even though they did not practice Wednesday. Antropov is still feeling the affects of a knee-to-knee collision suffered Saturday in the Rangers' 1-0 loss in Boston. ... The Rangers scratched LW Aaron Voros. The Flyers scratches were LW Riley Cote (finger injury) and D Ryan Parent. ... The teams will finish the regular season Sunday in Philadelphia.
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