The Capitals took a 2-1 lead when Evgeny Kuznetsov passed to Mantha in the right circle and his shot deflected in off Montembeault at 11:43.
Oshie increased the lead to 3-1 when he knocked in his own rebound for the Capitals' first power-play goal of the season at 15:20.
"I think we were moving the puck around better, a little crisper, little more direct," Oshie said of the power play. "Pretty lucky positioning on my goal. Had to go switch out sticks mid-play there and walked right into a puck sitting there for me."
Washington was 1-for-2 on the power play; Montreal was 0-for-3.
Ovechkin hit the right post trying to score on an empty net with a minute left.
"They kind of took it to us in the second, where I thought we had a good start in the first and obviously a good third period," said Canadiens forward Jonathan Drouin, who played 15:16 in his season debut. "It kind of stings that way but they're a team with experience and a lot of chemistry and they're going to find ways to get goals."
NOTES:Canadiens rookie defenseman Arber Xhekaj had an assist for his first NHL point. … Montreal center Sean Monahan won 9-of-13 face-offs. … Oshie's 61 power-play goals since joining Washington in 2015-16 rank second on the team in that span behind Ovechkin (109). … With his assist on Oshie's goal, Ovechkin has 244 power-play assists, seventh among active players.