With Rick Nash off for tripping, Martin Erat sent a pass to Green at the point for a one-timed shot that got past Talbot on the glove side at 6:55 for his third goal.
New York lost defenseman Anton Stralman to an undisclosed injury in the period and played the remainder of the game with five defensemen.
"You go from six to five defensemen and you're top three have to log a tremendous amount of minutes," Rangers coach Alain Vigneault said, "Might make it a little bit more challenging in terms of defending and attacking, but that's not an excuse. Those are things that happen."
The Rangers tied it on a power play when Pouliot deflected Brad Richards' shot from the point past Grubauer at 1:37 of the second period. It was Pouliot's sixth goal of the season and third in four games.
The Capitals appeared to retake the lead midway through the second, but a replay review showed that Fehr's shot bounced off the post, went behind Talbot, but didn't cross the goal line.
After a flurry of saves by Grubauer late in the period, the Capitals went ahead 2-1 when Steve Olesky pushed a loose puck ahead to Backstrom. Talbot could only get a piece of the shot from the right circle that produced Backstrom's 10th goal with 1:05 left in the period.
"He's playing great, he's obviously in a groove," Oates said. "We count on him so much for so many touches in a game."
Lundqvist, a three-time All-Star, signed a seven-year, $59.5 million contract extension on Dec. 4 to become the highest paid NHL goalie.
Since then, he is 2-4-2 with a 3.41 goals-against average in eight games. Lundqvist lost his most recent appearance 5-3 to the New York Islanders last Friday, giving up four goals on 19 shots.
NOTES: Alex Ovechkin failed to score a goal for the ninth straight game against the Rangers, including the playoffs. ... Capitals C Brooks Laich (groin), who returned Monday after missing 11 games, was out of the lineup. ... RW Erat has 14 assists in 35 games, but hasn't scored a goal.