Ryan Callahan had pulled the Rangers into a 2-2 tie 6:58 into the final frame when he scored on a deflected shot that beat Caps goalie Braden Holtby to the stick side.
Ovechkin unleashed a wrist shot from high in the slot that sailed past a screened Henrik Lundqvist 5 1/2 minutes later, and Washington hung on to forge a 1-1 tie in their Eastern Conference semifinal series.
The Rangers' Michael Del Zotto clanged a shot off the post in the final minute after Lundqvist was pulled to add an extra attacker.
Lundqvist finished with 22 saves.
Game 3 is set for Wednesday in Washington.