Chris Kreider gave New York a 1-0 lead at 7:00 of the first period. Thompson tried to clear the puck after a dump-in, but Kreider intercepted it and scored from the high slot.
Strome tied it 1-1 during a power play at 18:46, tucking in the rebound after Quick stopped Chychrun’s shot from the point.
Lars Eller gave Washington a 2-1 lead at 2:29 of the second period, deflecting Martin Fehervary’s shot from the left point.
Mangiapane made it 3-1 at 10:08 when he scored from the bottom of the right circle off a pass across the slot from Nic Dowd.
Will Cuylle appeared to pull the Rangers within 3-2 at 13:04, but the Capitals successfully challenged that Brett Berard preceded the puck into the zone.
“That’s a frustrating point,” New York coach Peter Laviolette said. “If the goal stands, then you’re going on the power play. That’s definitely a swing.”
Sam Carrick cut it to 3-2, scoring alone in front at 16:26.
McMichael increased the lead to 4-2 at 18:13, redirecting a pass from Strome from the slot during a power play.
“Our guys did a tremendous job of responding in the second period and finding a way to flip that game, because it wasn’t looking good in the first period,” Capitals coach Spencer Carbery said. “I felt that we took over, certainly in the first half of the second period and then built the lead.”