Backstrom also netted the Capitals' first goal against Sabres goaltender Ryan Miller. Mike Green and Matt Hendricks also scored, with Hendricks tying the game 3-3 with 6:27 remaining in the third period.
Tomas Vokoun made 29 saves for Washington.
The Sabres fly to Germany on Saturday for a preseason game Tuesday in Mannheim. They'll open the season next Friday in Helsinki against Anaheim.
Washington plays its final preseason game Sunday against Chicago and opens its season against Carolina on Oct. 8.