The teams will play again here Tuesday.
Pittsburgh scored three straight goals in 1:01 in the first period after Mika Zibanejad put New York ahead 1-0 at 1:18 on the first shot of the game. It was Zibanejad's first even-strength goal this season.
"That's obviously the start you would like to get, an early goal like that," Zibanejad. "Didn't really matter in this game. We'll just move on."
John Marino tied it 1-1 at 16:13, two seconds after a Penguins power play expired. He scored his first goal of the season with a wrist shot past a screen from Evan Rodrigues.
Kapanen scored on a breakaway to give the Penguins a 2-1 lead at 16:52. From the far wall in the neutral zone, Jared McCann backhanded the puck past defenseman K'Andre Miller for Kapanen, who scored on a wrist shot.
Crosby made it 3-1 at 17:14. After taking a pass from Brian Dumoulin, Crosby split defensemen Ryan Lindgren and Adam Fox before scoring with a snap shot.
"We just talked about playing the game the right way," Sullivan said. "Playing on our toes and defending hard when we needed to. But from a mindset standpoint, continuing to try to score goals. We certainly don't want to be a team that sits on leads."
Georgiev, who made 24 saves in a 6-3 win against the New Jersey Devils on Saturday, was pulled following Crosby's goal.
Kinkaid's first save came at 4:10 of the second period against Jake Guentzel on a breakaway.
Zibanejad nearly got the Rangers within one goal, but he missed an open net with a backhand off the left post at 17:47.
"I think we tried regrouping the best we could in between periods," New York defenseman Jacob Trouba said. "We talked about how we liked the majority of our first period. Give them some credit too. They got a lead and they played a pretty tight game defensively and shut it down … There are two teams on the ice. It's not just us doing whatever we want."
Malkin tapped in a pass from Kapanen on a 2-on-1 to make it 4-1 at 13:57 of the third period.
Zach Aston-Reese extended it to 5-1 at 16:37 when he swatted the puck out of midair into Georgiev before scoring with a backhand from the side of the net.
NOTES: McCann did not play in the third period because of an upper-body injury. … The Penguins' three goals in 1:01 were the fastest in the NHL this season. They scored the second-fastest three goals Thursday in the first period of a 4-3 loss to the Philadelphia Flyers (1:11). … It was DeSmith's first win since Feb. 11. Tristan Jarry started 10 of the previous 11 games, including a 4-3 win against Philadelphia on Saturday. ... Trouba was minus-1 with an assist in 21:32 in his return after missing eight games with a broken thumb. … Kinkaid had not played in the NHL since Nov. 30, 2019, when he made 25 saves for the Montreal Canadiens in a 4-3 overtime loss to the Flyers.