The 23-year-old made 31 saves for his second shutout of the season as the Capitals blanked the Canadiens 3-0 on Wednesday night.
The Bell Centre crowd of 21,273, who can sense a playoff spot slipping away, booed as Montreal's league-worst power play went 0-for-7.
''I was a little frustrated, especially with the power play,'' said coach Randy Cunneyworth, whose team is 4-9-1 since he replaced the fired Jacques Martin behind the bench. ''It's largely my responsibility and we need better results.''
Montreal (17-21-8) is 1-3-1 in its last five and is nine points out of the eighth and final playoff spot in the Eastern Conference. But Cunneyworth said his club is far from throwing in the towel on the season.
''I don't believe that for one second,'' he said. ''We intend to come out with everything we have and tonight we had a couple of guys that didn't quite have it. If we could get that first goal it would have given us the hope and life we need and we didn't get it.''
Mathieu Perreault and Marcus Johansson scored early for Washington (25-18-2) and Alex Ovechkin added a power play goal in the second period as the Caps bounced back from a 3-0 loss at home to the New York Islanders on Tuesday night.
It was their fourth win in their last five games.
''It was two huge goals in the first period that gave us the lead and on that power play goal, (Troy) Brouwer did a great job in front of the net,'' sad Ovechkin, whose team was held to only 16 shots. ''If we had a shot it was pretty dangerous.''
Neuvirth, with his sixth career shutout, had to be sharp in the third period as the Canadiens pressed during a run of power plays and had 17 shots but couldn't find the net. Max Pacioretty had six shots while Scott Gomez and Erik Cole had five apiece for Montreal.
The Capitals, who won 59 per cent of face-offs, have a new commitment to defence under coach Dale Hunter, now 13-9-1 since he replaced Bruce Boudreau behind their bench. They did well to block 25 shots and limit rebounds and second chances by Montreal.
It was almost the reverse of the teams' playoff series two seasons ago, when the Montreal defence and their goalie at the time Jaroslav Halak held off the high-flying Washington attack for a first-round upset.
''I think we're all right (mentally), but obviously this is frustrating,'' said defenceman Josh Gorges. ''We're not going to give up hope or believing. It's tough now because we needed these two points. But we have to forget it. We have a huge weekend ahead of us.''
The Canadiens play Friday night in Pittsburgh and then face the Maple Leafs on Saturday night in Toronto.
Some unfinished business was settled almost immediately as newly acquired Rene Bourque faced the Capitals for the first time since he was suspended five games for elbowing star centre Nicklas Backstrom in the jaw. Backstrom is not expected back from his concussion until after the all-star break.
Bourque dropped the gloves off a faceoff at 1:15 and then won a lively bout with Matt Hendricks.
''I knew it would happen at some point,'' said Bourque, in his second game since he was acquired from the Calgary Flames. ''I have to take responsibility for what I did and I might as well get it out of the way early.''
''There was no talk,'' said Hendricks. ''I know my job here is to be that kind of a player. It's the code, the rules of the game. There are consequences for actions. He knows it as well. I'm sure he wanted it out of the way and it was good for us. It got us in the game.''
Carey Price had a rough start, allowing two goals on his first four shots, but only the Johansson goal was soft. As has happened often this season, it was the attack that let the goaltender down.
Drummondville, Que., native Perreault, back in the lineup after sitting out three games, scored 4:41 in when he put a shot between Gorges legs and inside the far post from the right circle.
Johansson fought off Andrei Kostitsyn's check to lift a soft shot over Price's glove at 8:23.
Ovechkin scored on a blast from the right point that found the far corner on a power play 10:44 into the second frame. It was his second in the last seven games and 19th of the season.
Notes: The Caps are 10-2-2 in their last 14 regular-season visits to Montreal. ... Petteri Nokelainen and Chris Campoli were scratched for Montreal, while the Caps sat out Jay Beagle, Jeff Schultz and Tomas Kundratek.