The Rangers, who trailed by two early in the first period, scored four goals in the third for the second time in three days against the Capitals; New York lost 5-4 at Capital One Arena on Sunday to open the two-game set.
Washington had its three-game winning streak end.
"It's certainly nice to draw from that experience where we know we can be a good third-period team and score goals," Rangers coach David Quinn said. "Anytime you can turn the clock back and draw from experience, especially something that happened so recently, it gives you more confidence to do it. I think our guys had that in the back of their minds."
Kaapo Kakko tied it 2-2 at 4:10, and Adam Fox gave New York a 3-2 lead at 6:32, extending his point streak to eight games (two goals, 13 assists). Panarin, who had an assist on each of those goals, made it 4-2 on a breakaway at 15:41. Pavel Buchnevich scored a shorthanded empty-net goal with 35 seconds left for the 5-2 final.
Filip Chytil scored, and Igor Shesterkin made 30 saves to help the Rangers (16-15-4) win for the first time in 11 games this season when trailing going into the third period.
"So big," Kakko said. "Washington is a good team and we need some points right now, so big win for us."