Nicklas Backstrom also scored for the Capitals (25-18-2), who had an eight-game winning streak stopped in Ottawa on Thursday but rebounded with their 13th win in their last 16 games.
They stretched their lead over Winnipeg for top spot in the Southeast Division to three points with three games to play.
Ovechkin took a step toward a third Rocket Richard Trophy as the NHL's top goal scorer with his 29th and 30th of the season. He has 20 goals in his last 18 games.
The Canadiens (27-13-5) ended a three-game stretch in which they conceded 18 goals with a 3-2 win over Tampa Bay on Thursday, but the same problems of lacklustre play and shaky goaltending returned with a vengeance in their final home game of the regular season.
The Capitals scored four goals on their first 11 shots on Carey Price. But while many among the 21,273 at the Bell Centre mockingly cheered routine saves, Price avoided being pulled for a third time in four starts.
Montreal has lost five of its last seven.
The Canadiens dominated the opening minutes and led 5-0 in shots when their worst fears came true.
A careless P.K. Subban went to Backstrom, who fed Ovechkin to fake a pass and beat Price with a low wrist shot, Washington's first of the game, at 4:49.
Mike Ribeiro, who had three assists, won a faceoff in the Montreal zone and Brouwer's long shot sailed past a screened Price only 1:08 later.
Brouwer, who has six goals in his last five games, got his second of the night on the Capitals' first shot of the second frame. Mike Ribeiro won a battle in a corner and Marcus Johansson fed it to the right circle for Brouwer's high shot that beat Price cleanly at 3:49.
Washington needed only 18 seconds on its first power play to score on a tic-tac-toe play from Mike Green at the point to Ovechkin in the left circle to Backstrom at the side of the crease at 7:50.
Ovechkin was parked in the left circle for a one-timer through Price's pads on Washington's second power play at 13:23 of the third.
Montreal ends the regular season with games in New Jersey, Winnipeg and Toronto.
Notes: Raphael Diaz returned after missing 25 games with a concussion and it was newcomer Davis Drewiske who sat out as Yannick Weber played a third game in a row. . . Brandon Prust was awarded the Jacques-Beauchamp Trophy as Montreal's unsung hero as voted by the local media. He returned after resting a bad shoulder for a game.
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