After Fleury had already stopped all five New York shooters, Sutter beat Lundqvist between the legs to secure the win.
The victory gave Pittsburgh wins in 10 of its past 11 games despite having a number of players out of the lineup. That list includes the Penguins top four defensemen and star center Evgeni Malkin, who are out with injuries, as well as All-Star wing James Neal, who served the final game of his five-game suspension Wednesday.
"To go through what we're going through and still find ways to win, I think it says a lot. That's not easy. It's really a combined effort from everyone to find a way," said Penguins captain Crosby, who had two assists. "It seems like it's someone different who steps up every night. I think the consistent things have been our goaltending and our defensive play."
That goaltending and defensive play came up big in overtime after Kunitz was called for goalie interference after running into Lundqvist 14 seconds into the extra period. The play left the Rangers goaltender down on the ice, but he remained in the game.
"A lot of times when you stick your head out like that and focus on the puck, it's kind of hard to take a hit. It just happened fast, I guess," Lundqvist said. "I expect to be pretty stiff and sore tomorrow. I'm just happy it wasn't worse than that. I didn't see him coming at all."
Pittsburgh killed off the penalty, setting the stage for the shootout.
"It felt like a long two minutes, that's for sure," Fleury said. "The guys did a good job helping me out."
Pittsburgh's penalty kill couldn't quite get the job done late in the third period, though. Down 3-2 late in the third, Matt Niskanen was whistled for high-sticking on Hagelin with 2:43 remaining in regulation. It was 57 seconds into Niskanen's minor when Brassard scored the tying goal. After Benoit Pouliot's one-timer from the right circle missed the net, the puck ricocheted behind the goal and straight to the streaking Brassard, who beat an out-of-position Fleury from a sharp angle with 1:46 remaining. It was Brassard's sixth goal of the season and marked the second time in two games that the Rangers had overcome a two-goal deficit.
"I think being down 3-1 we were in a tough spot, but we kept fighting and that's a good sign," Lundqvist said. "I feel like the last two games we're making progress."
Pittsburgh earned a 2-1 lead 5:25 into the third after Kunitz muscled the puck away from Ryan McDonagh, who moments earlier had his stick broken by an apparent Kunitz slash. From behind the Rangers' net, Kunitz found Crosby in the left circle. As the Rangers defense keyed on the Penguins center, Crosby found Dupuis by the side of the net, where he beat Lundqvist for his sixth goal of the season.
Sutter gave Pittsburgh a two-goal lead 61 seconds later. With Harry Zolnierczyk and Derek Dorsett each off for roughing, he carried the puck from his own blue line and into the Rangers zone before beating Michael Del Zotto to the inside and scoring on a backhand shot for his seventh of the season.
"Any time you get a 1-on-1, especially 4-on-4, you want to try to make a play on it," Sutter said. "I just tried to drive wide to get the D to think I was going to go wide or shoot. I tried to pull it in. Sometimes it works, sometimes it doesn't. It worked pretty well tonight."
Zuccarello cued New York's comeback with 7:17 remaining in regulation after John Moore's shot off the rush was stopped by Fleury, but trickled behind him before resting in the crease. Zuccarello got his stick on the loose puck while battling at the side of the net with Zach Sill to earn his seventh of the season and give the Rangers new life.
It was with McDonagh off for tripping Crosby on a partial breakaway that the Penguins opened the scoring 12:44 into the second. Jussi Jokinen was stopped from in close, but Kunitz stormed the crease in the ensuing scramble and managed to poke the puck past Lundqvist and into the net.
It was a similarly aggressive play around the Rangers net that drew a cross-checking penalty on Del Zotto and unsportsmanlike conduct penalty on Zolnierczyk with 6:10 left in the second period. With 15 seconds remaining in 4-on-4 play, Hagelin took John Moore's outlet pass at his blue line and sped by Simon Despres before going to the backhand and tucking the puck between Fleury's legs. Hagelin's seventh of the season tied the game 1-1 with 4:25 to play in the second.
Hagelin's hustle on his second goal in two games earned him praise from Rangers coach Alain Vigneault.
"I thought Hags, with his speed, was a positive factor in the game," Vigneault said. "He could challenge their defense with his speed wide and he got a goal by beating one of their defensemen. I figured we would just use that element and get him a little bit more ice time."
It was all a prelude to an entertaining and eventful third period, overtime and shootout.
"From the penalties to the power-play goal they scored to tie the game, then to have to kill of the 4-on-3 in overtime, it was a wild finish," Penguins coach Dan Bylsma said.