It was Mrazek's fourth shutout of the season and third in his past eight starts.
"I felt pretty good," Mrazek said. "Two big points on the line. The result, that's what we wanted. Every game means a lot, it's a lot on the line. Doesn't matter where we are right now. We have to keep grinding and keep working hard."
WATCH: [All Hurricanes vs. Avalanche highlights]
Andrei Svechnikov had two goals and an assist, Dougie Hamilton scored, and Teuvo Teravainen had two assists for the Hurricanes (38-24-7), who are 7-1-1 in their past nine games and are tied in points with the Pittsburgh Penguins.
"That was special," Hurricanes coach Rod Brind'Amour said. "I haven't seen some of those saves in a game. We gave up a little too much, obviously, but [Avalanche goalie Philipp Grubauer] made some saves, too. It was a good game, it was back and forth. They've got a good group and talent over there. At the end of the day, [Mrazek] has been solid all year."
Grubauer made 30 saves for the Avalanche (30-28-12), who have lost four of their past six games (2-4-0) and trail the Minnesota Wild by two points for the second wild card into the Stanley Cup Playoffs from the Western Conference.
"We got to capitalize on our chances," Grubauer said. "Overall, it was a good game. They're a really skilled team, very offensive oriented. We got some chances, too, but we got to keep playing and chip away, chip away. We missed out on two important points."