Ilya Samsonov made 17 saves for the Capitals (28-16-9), who had won five straight on the road and were playing their first game since Feb. 17.
"Maybe they got the bounces and we didn't, but it's a battle at the net-front, and I think tonight it's something they kind of outdid us in a little bit," Washington defenseman Nick Jensen said.
Zibanejad gave the Rangers a 1-0 lead at 12:57 of the first period, scoring his 20th goal of the season on a one-timer from the top of the right circle off a drop pass from Lafreniere on the rush.
"I tried to be an option for him, hoping that he sees me, and he did, obviously," Zibanejad said. "He's a really smart hockey player, sees the ice really well. I'm not surprised I got that pass from him."
Shesterkin stopped Garnet Hathaway on a breakaway at 5:10 of the second period.
Lafreniere made it 2-0 at 18:48 when he redirected Ryan Lindgren's shot from the left point after a Capitals turnover.
"I thought the first period was a pretty even hockey game," Washington coach Peter Laviolette said. "The second period was really the same. I don't like the goal right at the end of the second. The game's tight, it's close and we kick one up there. That's a tough one to give up."