Cole Caufield scored his first goal since Nov. 24 for Montreal (8-31-7), which has lost eight straight (0-6-2). Cayden Primeau was pulled at 5:18 of the second period after allowing four goals on 14 shots. Sam Montembeault made eight saves in relief.
St. Louis made his NHL coaching debut after he was hired to replace Dominique Ducharme, who was fired Wednesday after a 7-1 loss to the New Jersey Devils on Tuesday.
"It was amazing," St. Louis said. "I just love how we fought and I just felt we kept getting better as the game went [on], and that was fun to see. … We didn't cheat, you know, we just stayed the course, and I really feel the only thing we didn't do tonight was win."
St. Louis spoke to his players for about 10 minutes when he met with them for the first time prior to an optional morning skate Thursday.
"He came in full of energy, it looked like he wanted to lace them up, so it was pretty exciting for all of us," Canadiens forward Josh Anderson said. "And you could see a couple of jaws drop with Marty, the way he talks and presents himself and the way he wants to work with the players and the organization, and he wants to build a winning culture. I'm not going to get into the gist of it, you know, what he said in detail, but it was a very good speech to the players."
Ovechkin was unable to travel to Canada due to pandemic restrictions in Quebec. He had an assist in a 5-4 loss to the Columbus Blue Jackets on Tuesday after missing one game in COVID-19 protocol.
Snively gave the Capitals a 1-0 lead at 5:04 of the first period when he drove to the slot and scored stick side on a big rebound of Justin Schultz's shot off Primeau's right pad.
"It's an amazing opportunity to play with Tom [Wilson], 'Kuzy' [Evgeny Kuznetsov] and last game got to play with [Nicklas] Backstrom," Snively said. "It's a privilege, and I'm just trying to make the most of it. I'm just having a lot of fun."
Connor McMichael scored 20 seconds later to put the Capitals up 2-0. He drove the left side and scored on a wrist shot from a sharp angle over Primeau's right shoulder at 5:24.
Carl Hagelin made it 3-0 at 3:40 of the second period before Rem Pitlick cut it to 3-1 at 4:09.
Snively pushed the lead to 4-1 at 5:18 and Montembeault replaced Primeau.
"I thought his game was really good tonight, but it's been good," Capitals coach Peter Laviolette said of the 26-year-old forward. "He's detailed, he's tenacious, he's quick, he's got a good skill level. You notice him in the battles, you notice him when he has open space, then you notice that he can make plays as well.
"It's not just tonight, he got rewarded with a couple goals tonight and an assist, but it's something we've noticed in most of the games and that's why he's up playing with 'Kuzy' and 'Willy.' He does a good job. He brings a lot of tenacity to the game."