Bondra was tied up in front of the Penguins goal by defenseman Neil Wilkinson, but spun out of his grasp and slipped a backhanded shot past goalie Tom Barrasso at 12:02.
Captials goaltender Rick Tabaracci made 12 saves over two periods, allowing only a power-play goal to Viktor Ignatjev.
Jan Bulis also scored for Washington (2-1), which handed the Penguins (1-2-2) their second straight loss.
Working from the left point, Tuomas Gronman feathered a pass along the blue line to Ignatjev, who one-timed the puck inside the right post at 8:11 of the first period.
Bulis' team-high third preseason goal tied the game at 3:16.