The Capitals ended a three-game losing streak and moved within three points of the Lightning for the lead in the Southeast Division. Tampa Bay had won its previous six games.
Ovechkin assisted on a goal by Nicklas Backstrom midway through the first period to forge a 1-1 tie. Brooks Laich put the Capitals in front 6:38 into the second and Ovechkin scored his 20th of the season on the power play less than 2 minutes later.
Washington went into the third period with a 3-2 lead and Backstrom scored again with 7:38 to go, assisted once more by Ovechkin. Jason Chimera tallied into an empty net with 38 seconds to play.
The win went to Semyon Varlamov, who made 23 saves.
Dwayne Roloson, who had recorded shutouts in his two previous starts, stopped 31-of-35 shots for Tampa Bay.
The four points for Ovechkin were his season high. The teams had split their previous four meetings.