Caps goalie Braden Holtby had a good night, making 29 saves, including some strong stops to deny the Rangers on second chance opportunities. Early in the second, he made a right pad stop on Kevin Hayes, who pounced on a rebound of a right point shot at the top of the paint.
Washington took its first lead of the night on its first power play chance early in the second. From the right wing corner, Brett Connolly threw the puck up high, and Carlson made a great keep at the point, lunging to flag the puck down on his backhand and then quickly sending a saucer pass to Alex Ovechkin. Perhaps even more amazingly, Ovechkin one-timed the short-hopped pass without settling it, and his drive eluded Lundqvist to give the Caps their first lead of the night at 3:32 of the second.
Just after the midpoint of the middle period, the Rangers drew even on a power play of their own. Five seconds after Dmitry Orlov was seated for holding, New York's Jimmy Vesey scored from the paint, pouncing on a loose puck after Devante Smith-Pelly blocked Neal Pionk's shot from the point.
The Caps regained the lead late in the frame when Ovechkin netted his second power-play goal of the period, this time one-timing a no-look Carlson feed past Lundqvist at 17:01.
New York had a flurry of late chances in the second, but Holtby held firm, enabling the Caps to take that 3-2 advantage into the third.
In the third, Washington exactly as a team with a one-goal lead should against a weary team, forechecking the Rangers hard and forcing some icing calls. This was a departure from the way the Caps played in the third on Saturday against Toronto, when the Leafs were able to take control and ultimately earn the win.
New York looked heavy-legged in the first half of the third, but Nathan Walker's poorly timed offensive-zone holding call at 9:20 gave the Blueshirts the man advantage, and they tied it up at 3-3 when Kreider tipped Pionk's point shot past Holtby at 10:25.
New York gained some jump from that development, and the two sides traded chances the rest of the way. The Rangers were able to kill off a late penalty on Hayes, and the game went into overtime.
Washington didn't manage the puck very well in the extra session, but it ultimately generated the only two shots of overtime, and Niskanen netted the game-winner. Seventeen of his 57 career goals have been game-winners, a remarkable percentage.