Callahan tapped in a perfect feed from Brandon Dubinsky on a 2-on-1 break for his fifth of the season and first in seven games. Dubinsky, who also assisted on Marc Staal's tying, short-handed goal with 1:26 left in regulation, made a nice move to get around defenseman Paul Martin before setting up Callahan.
"It was an amazing play by Dubie to draw the defenseman to slide, pull around him, freeze [goalie Marc-Andre Fleury]," Callahan said. "I think that was the easiest goal I've ever scored."
Pittsburgh's Chris Kunitz and Matt Cooke scored 38 seconds apart in the final 2:31 of regulation, turning what could have been Lundqvist's third shutout in six starts into a potential loss and causing the veteran Swedish goaltender to break his stick on the crossbar in disgust.
Lundqvist was whistled for unsportsmanlike conduct for slamming his stick.
"I'm still angry -- even though we scored," said Lundqvist, referring in part to the fact the Penguins were given three third-period power plays and the Rangers didn't have any in the game. "But it's hockey. Things happened so fast, everything changed. I've got to stay cooler, obviously, but it felt like they got another chance after chance to get back in the game. I felt like it wasn't fair, but the game is over and you just have to deal with it."
Moments after Lundqvist skated to the bench for an extra attacker and 27 seconds after Cooke's goal, Staal tied it with a one-timer off a pass from Dubinsky.
"It was a lot of hockey packed into the last three minutes," Pittsburgh coach Dan Bylsma said. "It didn't happen in the first 57. It looked like it was going to be a 0-0 or 1-0 type of game, and it ends up with three goals there."
Erik Christensen gave the Rangers a 1-0 lead in the second period. New York protected that advantage until a wild final 2 1/2 minutes of regulation and overtime.
"There was nothing really going on most of the game, and then the last five minutes ... it was pretty crazy," Staal said.
Lundqvist was superb in his return after missing two games with an illness. He stopped the first 36 shots he faced until Kunitz beat him for his fifth goal. Kunitz roofed a loose puck in the slot to tie it.
Cooke looked to have the winner with 1:53 to play, taking a pass from Pascal Dupuis just inside the blue line, skating down left wing and beating Lundqvist with a wrist shot for his fourth goal.
Lundqvist made several quality saves as Pittsburgh held a 39-25 shots advantage and generally had the better of the play.
"Hank made some huge saves, which is what you have to do against a team like that," Rangers coach John Tortorella said.
The Penguins outshot the Rangers 20-7 in the first half of the game, but New York grabbed the lead on Christensen's third goal at 10:16 of the second.
Christensen, stationed in front, picked up a rebound while skating to the right circle, turned around and fired a shot that deflected off the skate of Pittsburgh defenseman Deryk Engelland and got past Fleury.
"We played well and did a lot of good things," Crosby said. "We made a couple of mistakes late and we were only able to get one point out of it, but we did a lot of good things."
Rangers D Dan Girardi left the game with 3:48 to play in the third after a puck struck him in the face, causing heavy bleeding that left a pool of blood on the ice along the boards near New York's bench. His injuries aren't believed to be serious. ... Crosby, who had a five-game goal streak snapped, assisted on Kunitz's goal, won his first 12 faceoffs and was 25 for 32 on draws. ... The Penguins are 8-0-2 in their past 10 against the Rangers. ... New York improved to 4-0 on the second of back-to-back games and 13-2-2 in such situations the past two seasons.