Toronto rallied with three goals in the third period to take a 4-3 lead, but gave up a power-play score by Semin with 5:38 remaining that forced overtime.
Ovechkin put a wrister past Jonas Gustavsson in the second round of the shootout and Semin clinched it with a slapshot. Michal Neuvirth was perfect in the shootout after stopping 24 shots in regulation and overtime.
Washington won for the fourth time in five games and Toronto lost its fourth straight.
Mike Brown, Kris Versteeg and Tyler Bozak all scored during the first 7:17 of the third period for the Maple Leafs after they went into the stanza facing a 3-1 deficit.
Gustavsson stopped 26 shots.