Semin broke free near the Tampa Bay net and redirected a pass from Nicklas Backstrom past goalie Johan Holmqvist at the 1:41 mark.
Washington left wing David Steckel opened the scoring 7:46 into the game, deflecting John Erskine's slapshot past Holmqvist.
Martin St. Louis tied it with a short-handed goal less than five minutes later, skating in alone on Capitals goalie Brent Johnson and backhanding the puck high into the net. Lightning center Vincent Lecavalier, who set up the goal, left in the second period with an undisclosed upper body injury.
Both goalies played the entire game, each making 18 saves.
Lightning defensemen Dan Boyle was injured in the locker room after the game. Distracted while he was hanging up his skate, it slipped off of the hook and hit him in his left wrist, cutting a tendon. Boyle was to have surgery on Sunday and will be out several weeks.
Before the game, the Lightning introduced Tampa attorney Steve Burton as a new partner to its prospective ownership group. The group is headed by former Columbus Blue Jackets general manager and former Florida Panthers coach Doug MacLean.