Ovechkin helped out on Mike Green's power-play marker 5:59 into the game and made it 2-0 Washington in the second period on a backhander past Henrik Lunqvist, helping the top-seeded Caps dispatch the Rangers and advance to the Eastern Conference semifinals.
Alexander Semin also scored and Michael Neuvirth turned aside 26-of-26 shots for the Capitals, who closed out the series after blowing a 3-games-to-1 lead in their previous post-season series last year against Montreal.
Washington will now go on to play the winner of the Philadelphia-Buffalo series.
Wojtek Wolski scored with 32 seconds left in the game, allowing the eighth-seeded Rangers to avoid a shutout.
Lundqvist, making his 31st consecutive start for New York, made 24 saves in the setback.