Backstrom already had four assists when he got to a loose puck near the left circle and snapped in his 24th goal of the season to make it 6-5 at 5:34 of the third. Washington scored three goals on the power play to offset a season-high four man-advantage goals by the Rangers.
Capitals captain Alex Ovechkin had two goals and an assist to reach 500 career NHL points. He is the fifth player to reach the milestone in five seasons, doing it in only 373 games.
Boyd Gordon, Mike Knuble and defenseman Tom Poti added goals for the Capitals, who haven't lost since Jan. 12 at Tampa Bay.
New York returned home from a 1-2 Western trip, but couldn't turn its best offensive output in eight games into a win. Vinny Prospal had two goals, and newly acquired forward Olli Jokinen, Brandon Dubinsky and Ryan Callahan also put pucks past goalie Jose Theodore. The Rangers lost in regulation for the seventh time in eight games.
Leading scorer Marian Gaborik had two assists, as did Jokinen and Prospal for New York. But Jokinen was also called for three penalties, including a hooking call against Poti that led to Backstrom's winning goal.
The Capitals, who lead the NHL in scoring, erased deficits of 1-0, 2-1 and 5-3. Then they held on, with the help of three power plays in the final 11 minutes.
The Rangers carried play in the first period and took a 1-0 lead at 8:58 when Callahan tipped in a shot in front by Jokinen, snapping New York's 0-for-25 power-play slump over seven games. Gordon tied it with 3:20 left in the frame, despite Washington being outshot 15-5 at the time.
Prospal got that one back just 10 seconds later, and New York finished the period with a 2-1 lead and an 18-6 advantage in the shots.
The tide turned in the second as Washington quickly caught up in shots and on the scoreboard. Knuble's 20th goal made it 2-2 at 4:41, and Ovechkin's power-play tally at 7:16 gave the Capitals their first lead.
Jokinen, in his second game since being acquired from Calgary on Monday, scored his 12th of the season and first with the Rangers to make it 3-3 at 12:19. Prospal put New York back on top just 40 seconds later.
Dubinsky's power-play goal with 1:12 left in the second made it 5-3 and had Madison Square Garden rocking.
It didn't last long as Ovechkin quieted the crowd by netting his NHL-leading 38th goal this season, scoring with only 8.5 seconds left in the middle frame.
Former Rangers defenseman Poti tied it 5-5 just 59 seconds into the third, 36 seconds after New York rookie Michael Del Zotto was sent off for high-sticking.
Notes
This was the Rangers' highest-scoring losing effort of the season. … Gaborik scored five of New York's six goals in the three-game road trip. … The Capitals have outscored opponents 57-27 during their streak. It is only the fourth time in the run that they allowed as many as three goals. … Backstrom entered the night sixth in the NHL in points and fifth in assists. He already as a career high in goals. … Washington was 3-for-9 on the power play. New York, which finished with a 38-32 edge in shots, was 4-for-6.