Beech circled behind the net and stuffed a wraparound shot past Flyers goalie Robert Esche, who finished with 32 saves.
Brent Johnson had 26 saves for the Capitals (3-1-1), who had two victories in four days over Philadelphia (1-5).
Reigning Calder Trophy winner Alexander Ovechkin had three shots in both the first and third periods, but did not score for Washington. Capitals centre Dainius Zubrus, a former Flyers player who underwent knee surgery during the off-season, made his pre-season debut and took two shots during his 19:45 on the ice.
Flyers defenceman Denis Gauthier was shaken up with 8:24 remaining in the second period when he took a knee to the head from Ovechkin. Gauthier was helped off the ice and did not return.