The 32-year-old forward was first or second on each of the 18 ballots. He led all players with 15 goals, the most in a single playoff year since Pittsburgh Penguins center Sidney Crosby had 15 in 2009, and finished with 27 points, second to linemate Evgeny Kuznetsov, who had 32 (12 goals, 20 assists).
"I think it is just like a dream," Ovechkin said. "It was a hard, long season. We fought through it. We worked so hard through all the years. ... It was the whole team, stick to the system, we didn't panic. ... We just had to push it and get the result done."
Ovechkin is the second player born in Russia to win the Conn Smythe; Pittsburgh center Evgeni Malkin won it in 2009. Ovechkin also is the first Russia-born player to be captain of a Cup-winning team.
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Kuznetsov finished second, earning five first-place votes and 13 second-place votes.
Capitals goaltender Braden Holtby received 17 of the 18 third-place votes after going 16-7 with a 2.16 goals-against average, a .922 save percentage and two shutouts. Golden Knights goaltender Marc-Andre Fleury received the other third-place vote.
Holtby said Ovechkin is the unquestioned leader of the Capitals.
"He came in and he realized the League has changed and he changed as well," he said. "He's been amazing for us. And he's just like the rest of us. We follow him because he knows one player doesn't make a team. If we were going to win this year, we needed every single person, and it started with him."