The next two shooters then missed, but Patrick Marleau extended the skills competition by slipping a wrister under Braden Holtby's pads.
However, Backstrom lifted a backhander over Niemi's glove at the other end, as Washington snapped an 0-11-1 skid at San Jose.
Eric Fehr and Chris Brown scored in regulation, while Holtby stopped 34 shots for the Capitals, who kept pace with the Red Wings for the final playoff spot in the Eastern Conference. Both teams have 79 points, one better than the Columbus Blue Jackets.
Marleau and James Sheppard scored for the Sharks, who saw Niemi make 23 saves in the loss, their second in the last three games.