"It is the way hockey goes," said Connor, who has six goals in his past four games. "You are going to get a couple of good bounces."
Connor put Winnipeg ahead 4-3 at 10:45 of the third period on a redirection of Neal Pionk's point shot on the power play before completing the hat trick when he got the rebound of Patrik Laine's shot and scored with a backhand to make it 5-3 at 16:31.
[WATCH: All Jets vs. Avalanche highlights]
After Blake Wheeler scored into an empty net to extend the lead to 6-3 at 17:39, Nazem Kadri scored for Colorado to cut it to 6-4 with 44 seconds remaining, but Nikolaj Ehlers scored into another empty net with 12 seconds left for the 7-4 final.
"He's dialed in," Wheeler said of Connor. "I mean, the kid's got world-class hands on him and he just works extremely hard. Since his recall a couple of years ago, he's just really invested in working every single night."
Wheeler had two goals and an assist, Mark Scheifele had a goal and three assists, Ehlers had a goal and two assists, and Connor Hellebuyck made 39 saves for the Jets (22-15-3), who were 0-2-1 in their previous three games.
"It wasn't always pretty, it wasn't always us carrying the play by any means," said Wheeler, who played his 900th NHL game. "You don't have to win in this League like that. You can just battle, and I think we had every guy invested in that battle. A lot of 1-on-1 battles we won tonight, and that was the difference."
Video: WPG@COL: Wheeler rips puck by Grubauer
Nathan MacKinnon scored two goals and Philipp Grubauer made 19 saves for the Avalanche (23-13-4), who are 0-2-1 in their past three games and 1-4-1 in their past six.
"We keep shooting (ourselves) in our own leg," Colorado forward Mikko Rantanen said. "We do mistakes on our own, you know? It's costing us right now, so we just have to figure it out. It's a tough division, tough conference, and we can't keep dropping these points."
Wheeler gave Winnipeg a 1-0 lead at 6:25 of the first period, receiving a cross-ice pass from Ehlers and scoring top shelf short side from the right circle.
MacKinnon tied it 1-1 at 9:43 when his point shot made it through traffic.
Video: WPG@COL: MacKinnon wrists one through traffic
Connor made it 2-1 at 8:27 of the second period. After a turnover by Cale Makar, Connor skated to the net and shot on Grubauer, who made the save but had the rebound go up over his shoulder and into the net.
MacKinnon tied it 2-2 at 13:47 with a one-timer glove side from the left face-off dot on the power play.
Scheifele gave the Jets a 3-2 lead at 14:53, taking a return pass from Pionk and scoring during a 4-on-4.
"We're not getting those easy goals," Avalanche coach Jared Bednar said. "We're working hard for what we get and we're giving up easy goals."
Video: WPG@COL: MacKinnon blasts one-timer for PPG
Gabriel Landeskog tied it 3-3 at 7:15 of the third period with a power-play goal after Connor was assessed a double minor for cross-checking Samuel Girard in the face at 5:05. Landeskog scored on a rebound after Tyson Jost's initial shot caromed to him off the end boards.
"I've got to control my stick a little better, but I was just trying to make a play and I ended up with four minutes," Connor said. "Especially watching them score, it's tough to sit there and watch that. But we battled back, and everybody top to bottom, we got efforts from everybody, so it was a good one."
Video: WPG@COL: Landeskog scores power-play goal
They said it
"That's a big number for sure. I've been here six full seasons and every day, every practice, every game I'm amazed at his ability to drive his body every single day. He plays a hard, grinding kind of game." -- Jets coach Paul Maurice on Blake Wheeler playing 900 NHL games
"We're finding different ways to lose every night lately and it's frustrating, so we got to figure our way out of it now." -- Avalanche defenseman Erik Johnson
"I didn't like our rush coverage and too many turnovers. Odd-man rushes, our [defense] had a tough night getting caught in the zone. They're capitalizing it seemed on every chance they got. The mistakes we made, we gave them home runs." -- Avalanche coach Jared Bednar
Video: Kyle Connor nets three versus the Avs
Need to know
MacKinnon passed Paul Stastny for ninth in Colorado/Quebec Nordiques history with 460 points (179 goals, 281 assists) in 496 games. … Scheifele has 20 points (nine goals, 11 assists) in his past 13 games. … Wheeler has 16 points (seven goals, nine assists) in his past 13 games. He has 51 points (19 goals, 32 assists) in 36 games against Colorado.
Jets: Host the Toronto Maple Leafs on Thursday (8 p.m. ET; TSN3, TSN4, NHL.TV)
Avalanche: Host the St. Louis Blues on Thursday (9:30 p.m. ET; NBCSN, NHL.TV)
Video: Connor's hat trick propels Jets past Avalanche