The Capitals ended a three-game skid and wound up with a 2-2-1 record on their five-game homestand.
Washington began the night two points behind Winnipeg for the eighth and final post-season spot in the Eastern Conference.
Tampa Bay held a 2-1 lead heading into the third period but Marcus Johansson tied it with 3:58 to go in regulation.
Ovechkin then beat Dustin Tokarski with the game-winning shot in the first career start for the Tampa Bay goaltender. Tokarski gave up three goals on 32 shots.
The win went to Tomas Vokoun, who made 24 saves.
Celebrity Families of 2014 [PHOTOS]