Anthony Beauvillier fed his own rebound in front to Ovechkin, who scored his first career Stanley Cup Playoff overtime goal after the Canadiens had rallied with two goals in the third period.
Game 2 of the best-of-7 series will be here on Wednesday (7 p.m., ESPN, MNMT, SN, TVAS, CBC).
Ovechkin also had an assist and Beauvillier had a goal and an assist for the Capitals, who are the No. 1 seed from the Metropolitan Division and in the Eastern Conference. Logan Thompson made 33 saves.
Sam Montembeault made 29 saves for the Canadiens, who are the second wild card from the East.
Cole Caufield pulled the Canadiens within 2-1 with a power-play goal at 10:32 of the third period. Patrik Laine’s shot from the left circle deflected off Capitals Nic Dowd and Matt Roy, and Caufield knocked in the loose puck from the slot.
Nick Suzuki tied it 2-2 at 15:45, when he controlled a loose puck during a scramble in front and, with Thompson out of his crease, lifted a wrist shot into the open net.
Ovechkin gave the Capitals a 1-0 lead at 18:34 of the first period, taking a pass from Tom Wilson and scoring a power-play goal on a wrist shot from the top of the left circle. It was his 73rd career playoff goal.
Beauvillier made it 2-0 at 12:09 of the second period. Montembeault made the save when Beauvillier tipped Ovechkin’s shot from the left point, but Beauvillier put the rebound between Montembeault’s pads.