Ovechkin scored in each of the first two periods to get to 42 this season. The Russian winger became the 20th player and fourth-fastest in NHL history to 600 goals and is on pace to lead the league in goals for the seventh time.
Kuznetsov made it a night of celebration for Washington by scoring on a breakaway 4:11 into overtime.
Behind a run of eight wins in 11 games overall, the Blue Jackets moved past idle New Jersey into the first wild-card position in the Eastern Conference. Columbus also pulled within two points of third-place Philadelphia in the Metropolitan Division.