The Rangers rallied from a 3-1 series deficit to advance to the Eastern Conference final, where they will meet either the Boston Bruins or Montreal Canadiens.
It was first time in 17 attempts New York have been able to come back in a series after trailing 3-1.
The Rangers will be making their second appearance in the conference finals in three years. They lost to the New Jersey Devils in 2011-12 in six games.
"What a feeling," Rangers' goaltender Lundqvist said.
"We battled so hard as a team the last three games. After losing that fourth game it was tough.
"When you face a challenge like that it's about how you answer and we just did it the right way. We came together as a group and played a really smart game."
Lundqvist showed his Game Seven magic again, raising his career record to 5-1 in those situations. He stopped a combined 102 of 105 shots in winning the final three games of the series.
"I thought in the first two periods, he played a real strong game when they had more shots," New York coach Alain Vigneault said.
"Then (the Penguins) took their game to another level in the third period and our goaltender took his game to another level and was able to stop a barrage of good opportunities."
The Penguins fell to 2-7 in their last nine Game Sevens at home.
Richards, 7-0 in Game Sevens in his career, put the Rangers ahead for good when he scored a power-play goal at 7:56 of the second period after taking a pass from Martin St. Louis with Penguins defenseman Matt Niskanen off for tripping.
The Rangers opened the scoring at 5:25 of the first period through Dan Boyle before Jussi Jokinen evened the score at 1-1 at 4:15 of the second.
- - -
Chicago Blackhawks star forward Patrick Kane scored off a fortunate bounce in overtime, lifting his team past the Minnesota Wild 2-1 to close out their best-of-seven play-off series 4-2 to advance to the Western Conference finals.
A dump-in shot hit a stanchion in the glass behind Wild goaltender Ilya Bryzgalov and bounced in front of the net. Kane pounced on the play, lifting a backhand shot into the upper reaches of the net, ending the series near the halfway mark of the first overtime.
Right winger Kris Versteeg also scored for Chicago, who benefited from 34 saves by goaltender Corey Crawford in handing Minnesota their only home playoff loss of the season.
Rookie left winger Eric Halua scored the Wild's only goal.
- Sports & Recreation
- Ice Hockey
- Montreal Canadiens
- Boston Bruins
- New Jersey Devils
- The Penguins