"Lots of chances, just couldn't put the puck in the back of the net," Golden Knights coach Gerard Gallant said. "It was one of those 6-5 hockey games and it ended up being 3-0 for them.
"I thought both goaltenders were outstanding. (Subban) gave us a chance to hang around in there. Varlamov made a lot of big saves."
The Avalanche took a 1-0 lead on Jost's goal at 6:36 of the first period. Jost forced Golden Knights forward Pierre-Edouard Bellemare into a turnover, gained possession between the hash marks and spun around for his first goal since Jan. 2 against San Jose.
Agozzino, who was recalled from Colorado of the American Hockey League on Sunday, made it 2-0 at 5:47 of the second period. Nathan MacKinnon dumped the puck off the sideboards and Gabriel Landeskog retrieved it in the right corner. He passed by Vegas defenseman Colin Miller to Agozzino in the slot for a one-timer inside the left post.
Agozzino, 28, had not played in the NHL since the 2015-16 season; he entered with three assists in 10 career games.
"I've been waiting a long time for that moment," Agozzino said. "It's special and tough to put into words. There was a lot emotion after I saw it go in and just pure excitement. I came up with the mindset to try to help this team, in whatever aspect it was. I'm glad I did that tonight to help this team to get a win. It's a big two points and a special night for me.
"I'm sure my dad is going to call me for (the puck). I'm sure it will go in a nice frame in my house, but he'll be fighting me for it."
Agozzino was leading his AHL team in scoring with 28 goals and 50 points in 48 games.
"He did a really nice job," Avalanche coach Jared Bednar said. "Smart, intelligent 200-foot player, made some plays, had some poise with the puck."
The Avalanche extended their lead to 3-0 when Calvert batted in the rebound of Matt Nieto's shot at 6:53 of the third period.
Varlamov made 15 saves in the third.
"I just don't think we were executing," Vegas forward Reilly Smith said. "It seemed like there were a lot of sloppy plays. I think we had a lot of chances where we had people open for scoring chances, but we couldn't get the puck there. Probably just got a little too frustrated."
Bednar broke up Colorado's top line of Landeskog, MacKinnon and Mikko Rantanen, placing each on a different line for the first time. MacKinnon centered left wing Alex Kerfoot and right wing Sven Andrighetto, Rantanen was at right wing with center Carl Soderberg and left wing Nieto, and Landeskog was on left wing with Jost at center and Calvert on the right.
"As a line they hadn't been doing a whole bunch lately and created a lot offensively," Bednar said.