Paul Postma scored the game-winning goal and Hutchinson made 35 saves, including 18 in a perfect third period, as the Jets hung on for a 5-3 win over the Calgary Flames.
"Especially with where I started at the start of the year, I didn't think it would be possible to be in the NHL," said Hutchinson, who played Winnipeg's final three games compiling a 2-1-0 record, 1.64 goals-against average and .943 save percentage.
Postma broke a 3-3 tie at 9:16 of the third, ripping a slapshot past Karri Ramo from the blue-line.
"There was a lot of traffic in front of the net and I just wanted to get it through. I took a shot, kept it low and it found a way into the back of the net," said Postma.
It then fell upon Hutchinson to preserve the lead as the Flames feverishly buzzed around the Jets end, outshooting the visitors 14-1 before Blake Wheeler put the game away with an empty net goal.
"I definitely had a lot of work in the third period but at the same time, our guys played hard in front and blocked a lot of shots," said the 24-year-old. "When your guys are working that hard in front of you, it gives you that added incentive to bear down and make those saves."
One of Hutchinson's biggest stops came with four minutes left when he threw out his glove to stab a shot from Kenny Agostino, who had been sent in alone.
"Hutch played so well for us these last three games. He’s got a bright future ahead of him and we’re looking forward to playing with him," Postma said.
Michael Frolik, Evander Kane and Carl Klingberg also scored for Winnipeg (37-35-10).
It was the final game of the season for the Jets. Going back to its days in Atlanta, the franchise has missed the playoffs the past seven years.
Jiri Hudler, Sean Monahan and Kris Russell scored for Calgary (35-39-7), which had its four-game winning streak snapped.
"We didn’t get the start that we wanted but by the middle of the second period after those two power-play goals, it seemed like the momentum shifted and we had a great third period," said Flames coach Bob Hartley. "We missed a few chances, we hit some posts. The boys were on a mission, they wanted that win for the fans but unfortunately we couldn’t get it done."
It was Calgary's final game at the Scotiabank Saddledome, where they finish up 19-19-3. After the game as the players saluted the fans with a wave of their sticks at centre ice, the appreciative crowd rose to their feet in a thundering ovation.
"It was cool that everyone stayed in the building. It’s been great all year. The support has been unbelievable," said Flames captain Mark Giordano.
Testament to how hard Calgary has played is its 49 one-goal games (25-18-7), which ties the NHL record set by Florida in 2010-11.
"We've really tried to establish a work ethic and an identity of being one of the hardest-working teams in the league," said veteran Flames centre Matt Stajan. "It's exciting for everybody and I'm glad the fans see that. But we know we have a lot of work ahead of us. No one is satisfied in here. We have to find a way to get at least 15 more points next year and get into the playoff picture."
Hartley is proud of how his team has played and says the fans are too.
"It’s mutual respect. It’s a great story between this team and the fans. We are all part of a great community and you can feel that pride," Hartley said. "It’s on me to keep that pride and keep that progression going. Despite the loss tonight I am really happy how we turned our season, especially at home. That’s where success starts."
Down 3-1 halfway through the second, the Flames got a great chance to get back in the game when they got a two-man advantage for 1:31. Mark Stuart put the Jets down two men when he caught Hudler in the face with a high stick.
Although just 1-for-9 with a two-man advantage coming into the game, this time Calgary took full advantage when Monahan scored at 11:46 and Russell tied it 24 seconds later.
Monahan's 22nd goal is the most by a Flames rookie in 24 years, dating back to 1989-90 when Paul Ranheim had 26 and Sergei Makarov had 24.
After Hudler's goal reduced the Jets lead to 2-1, Winnipeg restored its two-goal cushion at 8:48 when Klingberg curled out from behind the net and wrapped in his first NHL goal.
The Jets scored twice in the first. Frolik on a deflection off of Flames defenceman TJ Brodie at 7:23 then Kane at 16:10 when he ripped a wrist shot into the top corner.
"I never ever put a lot of stock into the last games when you're out, except if they quit on each other, if they just say 'It's fine,'" said Winnipeg coach Paul Maurice. "They didn't quit and there was nothing on the line."
Ramo had 22 stops to see his record fall to 17-14-4.
Notes: Rookie Jets D Jacob Trouba left the game halfway through the first period after a shot from Paul Byron hit his own stick blade and struck him in the face. He did not return... Calgary C Mike Cammalleri (virus) did not play... Maurice finishes the year 18-12-5 after taking over as Winnipeg's head coach on Jan. 12... Flames signed Hobey Baker winner Johnny Gaudreau and his Boston College linemate Bill Arnold. Both will join the team for practice Saturday in Vancouver and will be in the line-up against the Canucks on Sunday.