Evgeni Malkin, who earlier in the overtime advantage struck a goal post and was robbed by Lundqvist's outstretched glove, finally got a puck past the goalie when his drive from the left circle bounced in off Rangers forward Brandon Dubinsky and Staal. It was the third Penguins goal that went in off a New York player.
"There were some bad bounces," Lundqvist said.
Pittsburgh held the Rangers to 16 shots overall and only one after the second period.
"We did some really good things. We deserved that one," Penguins captain Sidney Crosby said. "We felt like it was only a matter of time before we were back into it.
"All the games the rest of the way are going to be intense like that, especially in divisional games."
Backup goalie Brent Johnson earned the victory, despite facing only four shots in place of Fleury. "It's a great win but honestly, all I had to do was make a couple of saves and the guys took it from there," Johnson said.
Chris Drury, Artem Anisimov, defenseman Michal Rozsival and Dubinsky scored for New York. Rozsival's first goal in 38 games gave the Rangers a 4-2 lead they couldn't hold.
Pittsburgh gained the initial advantage when Marc Staal was whistled for interference on Crosby. Lundqvist jawed at the Penguins captain behind the net and then received a cross-check to the chest from Crosby. Dubinsky rushed in to deal with Crosby to create a big scrum.
"I didn't like the fact he came over," Crosby said of Lundqvist. "I thought it wasn't right. I got a cross check in the ribs that didn't feel too good. The last thing I expected was him standing over me. I let him know how I feel."
The Rangers were without leading scorer Marian Gaborik, believed to have a groin injury sustained during the Olympics.
In other games:
* At Glendale, Ariz., Wojtek Wolski scored with 23 seconds remaining in the game to break a 1-1 tie and lead the Phoenix Coyotes to a 3-1 victory over the Colorado Avalanche.
* At Dallas, Paul Kariya scored twice, combining with teammate Brad Boyes for a pair of goals during a 17-second span of the first period, and the St. Louis Blues extended their winning streak to a season-best five games with a 6-1 win over the Stars.
* At Nashville, J.P. Dumont, Jason Arnott, Marcel Goc and Jerred Smithson scored, and Pekka Rinne made 20 saves in the Predators' 4-2 victory over the Los Angeles Kings.
* At Boston, U.S. Olympian Tim Thomas made 24 saves in regulation and overtime and added three more in the shootout to lead the Bruins to a 3-2 victory over the Toronto Maple Leafs.
* At Atlanta, Nik Antropov had two goals and an assist, and Clarke MacArthur and Evgeny Artyukhin scored in their Atlanta debuts to help the Thrashers beat the Islanders, 6-3.
* At Washington, Scott Walker scored twice in a 3-minute span in the third period in his first game with the Capitals, who earned a 5-4 victory over the Tampa Bay Lightning. Mike Knuble had two goals in the second period for the Caps, who have won 12 straight home games.
* At Raleigh, N.C., Tom Kostopoulos and Rod Brind'Amour scored about a minute apart in the first period, Manny Legace made 25 saves and the Carolina Hurricanes beat Ottawa, 4-1, for their seventh straight victory.