Richards' goal in the third round of the tiebreaker Friday night gave the Rangers a 4-3 victory, the Penguins' first shootout defeat since a 3-2 loss to the Montreal Canadiens on Feb. 7, 2012.
Mats Zuccarello scored in the second round of the shootout for the Rangers. Evgeni Malkin matched that by beating Henrik Lundqvist to start the third round, but Richards zipped a wrister past Marc-Andre Fleury to end Pittsburgh's nine-game winning streak in the tiebreaker.
The Rangers, who lost 2-1 to the Edmonton Oilers in New York on Thursday, failed to hold three one-goal leads but went home with two points thanks to Richards' deciding goal.
"We played a real solid game," Richards said. "We didn't do that last night, so that's when you put bounces and bad chances or bad luck into play, but they're a good team. We played hard.
"They're going to get goals sometimes, that stuff happens, but we gave ourselves a chance to win."
It was the final game for each team before the Olympic break. Seven Rangers and seven Penguins will take part in the 2014 Sochi Olympics, and Penguins coach Dan Bylsma will be behind the bench for the United States.
Fleury is arguably the most successful goaltender in the eight-plus seasons the NHL has used the shootout -- he's 42-18 (.700), and his .770 save percentage is the best among all goaltenders who've seen 50 or more shots. Still, he said, he would rather avoid shootouts due to their unpredictability.
"Maybe it wasn't our best game of the season, but we found a way to hang on a get back into it," Fleury said. "It's always a little risky when you go to a shootout, but it's our first loss this year."
The Rangers were less than three minutes away from winning in regulation before Penguins forward James Neal tied the game with 2:56 remaining. Rookie defenseman Olli Maatta won the puck out of the corner and slid a pass to Neal to the left of the net. Neal wristed a shot past Lundqvist for his 20th goal of the season.
The Rangers broke a 2-2 tie 9:24 into the third period. Dan Girardi's shot ricocheted off the end boards; Benoit Pouliot collected the puck and tucked it in between Fleury's right pad and the left post for his 11th goal of the season and second of the game.
Despite allowing more than one goal for the first time in three starts, Lundqvist made 26 saves to extend his season-high winning streak to five games. The Rangers (32-24-3) have won five of six and reached the Olympic break second in the Metropolitan Division, though they trail Pittsburgh (40-15-3) by 16 points.
Lundqvist said he thought New York responded well after losing to the Oilers 24 hours earlier.
"I thought we deserved this win with the way that we played the whole game," Lundqvist said. "They're a good team. You can tell they have a lot of skill and they rely on their skill too. It was a night where it was about the special teams and we came up big.
"It was an important game for us after what happened last night."
Rangers coach Alain Vigneault agreed and said the Rangers needed to improve on their performance against Edmonton in order to have a chance against Pittsburgh.
"We definitely played better than we played last night," Vigneault said. "I thought we played with more energy and were more focused and with more purpose to out game and we had to. We were playing against such a strong opponent that we had to bring our A-game to the table."
After the first period ended 1-1, New York regained the lead 34 seconds into the second.
With Neal in the penalty box for interference, Girardi scored off of a faceoff win by Derick Brassard, snapping a shot past Fleury four seconds into the power play. It was the first power-play goal allowed by Pittsburgh in nine home games. The Penguins had killed 27 consecutive power plays at Consol Energy Center. Fleury faced 32 shots through two periods, seven more than he saw in each of his two previous starts. He finished with 38 saves.
The Penguins answered with a power-play goal at 8:29. Malkin took a pass from Matt Niskanen and skated to the right edge of the right circle before sending a pass to Neal near the circle's left edge. Neal sent a return feed to Malkin, who one-timed a slap shot past Lundqvist for his 18th goal of the season.
Malkin and Neal each extended their point streaks to five games. Pittsburgh's top-ranked power-play unit (25.4 percent) converted on two of its four chances.
"It was not a good game for us," Malkin said. "We tried to play better and we're lucky to take one point, but the last 10 minutes I thought we played better. But we need to play 60 minutes."
The first period followed a similar script; New York scored an early goal and the Penguins answered with a power-play goal to tie the game midway through the period.
Pouliot got the Rangers off to a quick start with a goal 1:04 into the game. Defenseman Marc Staal sent a shot from the point into the crease, where Zuccarello collected the rebound and tried to wrap it around the left side of the net. The puck was wedged between the left post and Fleury's skate until Pouliot poked it past the goal line.
Maatta tied it at 11:43 with his first career power-play goal. Defenseman Paul Martin slapped a shot into traffic in front of Lundqvist and Jussi Jokinen deflected the puck to the right of the net. It slid past Malkin to Crosby, who backhanded a shot on Lundqvist. Maatta finished the play by backhanding the rebound into the back of the net.
Bylsma said he thought his team performed better than it had in each of its three games before a 5-1 win against the Buffalo Sabres on Wednesday -- despite winning two of those games.
"I think we've come a ways from adjusting to getting guys back in the lineup," Bylsma said. "Better play all-around, but disappointing to go out with a loss here."