The Capitals moved from eighth to seventh place in the final Eastern Conference standings, leaving them with a first-round playoff matchup against defending Stanley Cup champion Boston.
New York began the final night of the regular season with a two-point lead over Vancouver in the race for the President's Trophy. The Canucks would win that trophy, symbolic of the best record in the league, with a point against Edmonton late Saturday.
Washington's win shoved Ottawa into eighth place in the playoff order, setting up the Senators as New York's first-round opponent.
Ovechkin scored 32 seconds into the game and Washington also picked up first-period goals from Mathieu Perreault and John Carlson.
Braden Holtby, who has appeared only 21 NHL games scattered over two seasons, made 35 saves for the Capitals.
With Tomas Vokoun and Michal Neuvirth both nursing injuries, Holtby could wind up starting for Washington as the playoffs open.
New York's Henrik Lundqvist allowed four goals on just 17 shots. Lundqvist finished the regular season with the third most wins in the NHL, the second-best goals-against average and the fourth-best save percentage.