Game 2 is Sunday.
Pittsburgh star Sidney Crosby was held without a goal for the 12th straight playoff game.
The Penguins have never lost a playoff series against the Rangers, rolling to victory in each of the four post-season meetings, including a 4-1 win in the Eastern Conference semifinals in 2008.
They split their four games during the regular season, all of them coming before the Olympic break. The Penguins have looked sluggish in the ensuing three months while the Rangers played their best hockey down the stretch before needing seven games to dispatch Philadelphia in the opening round.
For a team that was supposed to be gassed playing for the third time in four days, the Rangers wasted little time jumping on the sloppy and surprisingly lifeless Penguins.
Pouliot gave New York the lead 5:04 into first period, capitalizing on a Pittsburgh turnover then splitting Penguins defenceman Olli Maatta and Matt Niskanen before firing a wrist shot that caromed off Fleury's right arm and into the net.
Richards doubled the lead late in the period with his third and easiest goal of the post-season. Carl Hagelin beat Maatta to a puck in the corner and fed it to Richards, who had enough time in front to go from his backhand to his forehand and flip the puck by an overmatched Fleury.
Whatever sluggishness the Penguins felt after a three-day layoff vanished in the second.
Stempniak cut the lead in half by taking a nice drop pass from Beau Bennett then streaking down the middle and beating Lundqvist with a backhand 7:15 into the period.
Neal tied it just over 6 minutes later thanks to a rare mistake by Lundqvist, who deflected Neal's into the air then had it glance off his back and into the net. Lundqvist pleaded with officials that Penguins forward Evgeni Malkin had interfered with him while trying to make the save, but replays showed Malkin's high-stick swat didn't come close to touching the puck.
NOTES: New York went 0 for 4 on the power play and is 0 for its last 25 with the man advantage. ... The Rangers held out F Chris Kreider once again. Kreider wore a non-contact jersey during Friday morning's skate and his return from a hand injury remains uncertain. ... Penguins D Brooks Orpik missed his third straight game with an undisclosed injury.
Follow AP Sports Writer Will Graves at www.twitter.com/WillGravesAP