WATCH: [All Avalanche vs. Golden Knights highlights]
"I've just been trying to work in practice and keep up with the pace with the guys," Dansk said. "Goalie coach Dave [Prior] has been on me quite a bit, keeping me strict with everything, all the details. It's been unexpected, but a lot of fun."
David Perron, Oscar Lindberg, Cody Eakin and James Neal scored in the second period, and Jonathan Marchessault, Erik Haula and William Carrier scored in the third.
Dansk got his first NHL shutout and has won three straight games since taking over for injured Malcolm Subban (lower body), who was replacing Marc-Andre Fleury (concussion).
Semyon Varlamov made 14 saves for the Avalanche (5-5-0).
Colorado outshot Vegas 10-1 in the first eight minutes of the second period but the Golden Knights scored four times on their next six shots.
Perron scored his third goal of the season at 8:50 off a turnover by Colorado forward Nail Yakupov at the blue line. Perron deked to his left and finished with a backhand for a 1-0 lead.
Lindberg forced a turnover by Avalanche forward Sven Andrighetto, moved the puck past defenseman Chris Bigras and shot the puck over Varlamov's head to give the Golden Knights a 2-0 lead at 12:19.
"Two of the first three goals were self-inflicted," Colorado coach Jared Bednar said. "We've got to be better with the puck in some of those areas when there's danger."
Eakin scored his first goal of the season at 15:33 off assists from Neal and Perron to make it 3-0. Neal scored his seventh goal in nine games at 18:16 for a 4-0 lead.