The win kept the Capitals (4-0) perfect in the preseason, while the Bruins fell to 1-3-1.
Backstrom, playing without usual wings Alex Ovechkin and Mike Knuble, beat Tim Thomas off a giveaway 10:28 into the game and then tipped home a shot by Jeff Schultz with 2:52 left in the second period.
Andrew Gordon and Matt Bradley made it 4-0 in the third period before Mark Recchi scored on the power play for the Bruins -- costing Dany Sabourin, a Bruins farmhand last season, and Braden Holtby a combined shutout.
Jason Chimera had two assists for Washington.
Thomas, playing his first game after undergoing offseason hip surgery, allowed four goals on 15 shots.
Tyler Seguin, the second pick in the June draft, played his first game as a center for the Bruins and didn't have a point. He had a goal and an assist in two previous games as a wing.
The Bruins left after the game for Belfast, Northern Ireland, where they will train for two days before playing an exhibition game. Then they move on to Prague for their final preseason game and open the season there with two games against the Phoenix Coyotes, Oct. 9 and 10.