Carolina's Tuomo Ruutu broke a scoreless tie with 36 seconds left in the middle period but Ovechkin deadlocked the contest just 47 seconds into the third with his 28th goal of the year.
The game-winner came on a wrist shot by Hendricks with 12:36 to play in regulation.
Braden Holtby made the narrow lead stand up with 40 saves, 16 in the final period. It was the fifth meeting between the teams this season and Washington has won them all. They have one game remaining against each other.
Cam Ward stopped 24 shots for Carolina, which has lost three in a row.
The Capitals climbed within two points of idle Philadelphia for the best record in the Eastern Conference.