Evan Rodrigues had two goals and an assist, Carter scored twice, and Sidney Crosby had two assists for the Penguins, the No. 3 seed from the Metropolitan Division. Domingue made 32 saves.
Igor Shesterkin allowed four goals on 15 shots before being replaced at the start of the second period for the Rangers, the No. 2 seed from the Metropolitan. Georgiev made 19 saves in relief.
"Igor has been outstanding," New York coach Gerard Gallant said. "Really, you look at it right now, and he's played 10 periods the last four and a half days, five days. ... I thought it was a good time to jump-start it."
Pittsburgh leads the best-of-7 series 2-1. Game 4 will be here Monday.
RELATED: [Complete Rangers vs. Penguins series coverage]
Frank Vatrano got the Rangers to within 4-2 at 6:51 of the second period, scoring on a one-timer from the right circle, and Panarin cut it to 4-3 at 7:58 with a shot over Domingue's right shoulder from the left circle.
Andrew Copp then tied it 4-4 with a shorthanded goal at 15:59. Kevin Rooney stole the puck from Kris Letang and skated in for a backhand, which produced a rebound that Copp batted into the open net.
"It might have been the worst period we've played in the series. Not might have been, it has been," Penguins coach Mike Sullivan said. "We got away from the game that's brought us success. That's just the human element of sports."