Tyson Jost and Matt Calvert also scored as the Avalanche won their first game at the Pepsi Center since Jan. 19. Agozzino also added an assist.
Malcolm Subban had 35 saves for a Golden Knights team that's now dropped eight of their last 11 games. Subban started back-to-back games for the first time all season with Vegas electing to rest Marc-Andre Fleury.
Calvert gave Colorado a three-goal cushion with 13:07 remaining. The play was reviewed when it appeared he knocked it in with his glove. But the officials ruled he last powered in the puck with his stick after it struck his glove.
The only blemish for the Avalanche was a lackluster power play. They switched things up in an effort to generate more chances, but failed to score on three opportunities. They're now 0 for 26 with the man-advantage over the last nine games.
Agozzino was recalled Sunday from Colorado of the AHL, where he led Eagles with 22 goals and 28 assists. In his 11th NHL game - and first since April 9, 2016 - the 28-year-old Agozzino pushed a shot past Subban off a pass from captain Gabriel Landeskog. It gave Colorado a 2-0 advantage in the second period. The assist marked the 400th career point for Landeskog.
Early in the first period, Jost stole the puck down low early and made a nifty spin move to score his first goal since Jan. 2. The young center was in such a scoring funk he was briefly sent to the minors for some more work. Jost celebrated his goal in style by dropping to a knee and skating toward the boards.
An early Colorado lead at home - a rare sight in recent games.
It hasn't exactly been home-sweet-home for the Avalanche this season with an 11-12-5 mark. This after such a dominant showing a season ago when their 28 home wins matched the franchise record set by the 2000-01 Stanley Cup championship squad.
''It's not like we go out there and don't want to play at home,'' defenseman Nikita Zadorov said. ''We're trying.''
NOTES: Vegas LW Tomas Nosek returned after not playing in the last three games. ... Avalanche F Colin Wilson (upper body) skated with the team Monday and could soon be available. ... D Ian Cole (upper body) remains sidelined indefinitely. ... Landeskog joins Tampa Bay's Nikita Kucherov as the only members of the 2011 NHL draft class to reach the 400-point plateau. ... Agozzino assisted on Calvert's goal. It was his fourth NHL assist. ... The shutout was No. 25 in Varlamov's career.
Golden Knights: Begin a four-game homestand Wednesday night against Boston.
Avalanche: Host Winnipeg on Wednesday night.
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