Ward drove to the net and tapped
Following a mostly ceremonial faceoff, the teams skirmished at center ice.
Ovechkin opened the scoring on a power play with 1:47 remaining in the first period. Jesper Fast tied it with 4:39 left in the third, tipping Kevin Hayes' shot past goalie Braden Holtby.
Holtby made 31 saves, and Lundqvist stopped 27 shots.
Game 2 is Saturday at Madison Square Garden.
The Capitals ended a two-game losing streak against New York in the playoffs. Washington also lost three of the four regular-season meetings with the Rangers.
In the first period, with New York center
Ovechkin's goal was Washington's first playoff score against Lundqvist in 138:13 dating to Game 6 of the 2013 East quarterfinals.