Hellebuyck, who has five shutouts, moved into a second-place tie with Nashville Predators goalie Pekka Rinne for most in the NHL. Tampa Bay Lightning goalie Andrei Vasilevskiy leads the NHL with seven.
"The team is playing really well in front of me," Hellebuyck said. "They're bringing it every night and you can tell. Guys are getting a little banged up, that means they're blocking shots and doing the right things. My hat is off to my teammates."
WATCH: [All Avalanche vs. Jets highlights]
Patrik Laine, Jack Roslovic and Nikolaj Ehlers scored, and Blake Wheeler had two assists for the Jets (31-13-9), who have a point in seven straight games (5-0-2).
Semyon Varlamov returned and made 29 saves for the Avalanche (28-19-4) after missing 11 games because of a lower-body injury he sustained Jan. 2.
"I thought [Varlamov] played great," Colorado coach Jared Bednar said. "It was great to see him back in the net and he was our best player tonight. So, we've got to regroup and get a day off and get ready for Tuesday against San Jose."
Colorado is 1-3-1 in five games after a 10-game winning streak.
Laine scored his 13th power-play goal on a one-timer at 2:27 of the first period. He tied Pittsburgh Penguins forward Evgeni Malkin for most power-play goals in the NHL.
Roslovic made it 2-0 with his second NHL goal at 5:17 of the third period. Wheeler's shot from the slot deflected off Roslovic and defenseman Tyson Barrie up in the air and over Varlamov.