Panarin scored an empty-net goal at 19:59 for the 3-1 final.
"We've got five of our last six points and we're hanging around," Quinn said. "We continue to do that, continue to improve and get guys' game back on track, we're going to be in the middle of it."
Zucker gave the Penguins a 1-0 lead at 9:05 of the first period.
Sidney Crosby tried to extend the lead with a backhanded lacrosse-style goal from behind the net at 1:10 of the second period, but his attempt hit off left post.
"I saw him picking up the puck," Shesterkin said. "With a player of Crosby's caliber, you always have to be ready."
Crosby also hit the crossbar with a backhand shot at 13:29 of the second.
The Rangers tied the game 1-1 on Kevin Rooney's 6-on-5 goal on a delayed penalty at 17:42 of the second period.
They kept the game tied by killing a tripping penalty on Ryan Lindgren at 19:03 of the second period, and preserved their 2-1 lead by killing a holding penalty on Julien Gauthier at 14:25 of the third.
"It's definitely a work in progress," Zucker said of the Penguins power play. "We're not happy with it. We're not happy with our special teams. We have to keep fixing it, but I believe in the guys in this room, that we're going to work on it and work hard on it, hold each other accountable from guy to guy, from coaches to players and players to coaches."
NOTES:Rangers defenseman Brendan Smith didn't return after he sustained an upper-body injury in a collision with Brandon Tanev at 17:15 of the first period. Quinn did not have an update. … Panarin played in his 400th NHL game and has 427 points (153 goals, 274 assists). Five undrafted players in NHL history have scored more points in their first 400 games than Panarin; Wayne Gretzky (935), Peter Stastny (607), Bobby Orr (508), Joe Mullen (453) and Adam Oates (433). … Ryan Strome played in his 500th NHL game. … Defenseman Anthony Bitetto and forward Jonny Brodzinski each made his Rangers debut. Bitetto had four hits and blocked two shots in 14:51, and Brodzinski had one shot in 7:33. … Crosby won 16 of his 23 face-offs (69.6 percent), and the Penguins won 34-of-48 (70.8 percent).