Benoit Pouliot scored twice in regulation for the Rangers, who bounced back from a home loss to Edmonton the night before and won for the fifth time in six games.
The Penguins had won all four of their previous shootouts this season and 14 of their past 15 overall.
Zuccarello, the second New York shooter in the tiebreaker, tucked a backhand under the pads of Marc-Andre Fleury — who had not allowed a shootout goal all season. Evgeni Malkin beat Henrik Lundqvist to extend the game before Richards flipped a shot past Fleury to end it.
I don't think it's really truly going to sink in until we drop the puck, to be honest. I know there's going to be a lot of smoke and mirrors with the media attention and all that. We came [Monday] and it was sort of a light day to get things organized. We just want to focus in on the business aspect, the game itself. That's what we're preparing to do. Get these next couple of days out of the way and it's game on.
— Lightning captain Steven Stamkos on playing in his first Stanley Cup Final