The six-foot-five defenceman scored at 1:23 of overtime as the Jets continued their push for the playoffs with a 4-3 victory over the Carolina Hurricanes.
Byfuglien beat Hurricanes netminder Justin Peters off a rebound from a shot by Andrew Ladd, who finished with three assists.
"Ladd was by himself and I just jumped up," said Byfuglien, who has eight goals and 17 assists this season. "I think he shot it off that pad on purpose and I got the rebound."
Carolina's Alexander Semin tied the game 3-3 with 1:12 left in the third period and Peters on the bench for an extra attacker, beating Jets goalie Ondrej Pavelec on the glove side.
Blake Wheeler had a goal and two assists, Zach Bogosian a goal and one assist and Paul Postma also scored for the Jets (23-19-2), who remained ninth in the Eastern Conference but moved to within two points of the Southeast Division-leading Washington Capitals.
Washington, which lost 3-1 to Ottawa on Thursday, has 50 points and the coveted automatic spot in the East Conference playoffs.
The New York Rangers are tied on points with Winnipeg, but hold down the final playoff spot in the East with a game in hand after a 6-1 victory over Florida.
Tuomo Ruutu scored Carolina's other goals, his first and second of the season coming in his 12th game with the Hurricanes (17-23-3). Jordan Staal had a pair of assists.
"I thought we had a really good push at the end," Ruutu said. "It's too bad that we couldn't get the win tonight."
The Jets have now won a season-high five straight games — the longest streak since they arrived in Winnipeg before last season — and they'll need to keep those winning ways on the weekend.
The club hosts the New York Islanders on Saturday in another key match. The Isles are in seventh place, three points ahead of the Jets.
"The next two points are huge for us and we've just got to take it a game at a time," said Bogosian, who has six points in his last three games, including five assists.
"We can't worry about other teams or what streaks we have going on."
A key to Winnipeg's success Thursday was the play of Pavelec, who made 24 stops, including one spectacular one in the second period that sparked the crowd at MTS Centre to give him a standing ovation.
Carolina defenceman Justin Faulk fired a wrist shot from close in at Pavelec, who whipped out his stick before smothering the loose puck.
Peters finished with 27 saves, including a breakaway stop on Byfuglien in the second when Winnipeg was ahead 1-0.
It was Postma, though, who beat Peters with a high shot over his glove with three seconds left on a power play to make it 2-0 at 8:27 of the period.
Ruutu scored with a shot that rang off the inside of the post on Pavelec's stick side and zipped across and into the netting at 10:38 to make it 2-1 heading into the third.
Hurricanes coach Kirk Muller, coaching in his 100th NHL game, wasn't surprised his team fought back from a 3-1 deficit midway through the third.
"That’s the way our guys have been playing," he said. "We haven't got the breaks or the results that we, to be honest, we really deserve in our performance in the last three, four weeks.
"So it's unfortunate because I'm really proud of the guys the way they've been battling, playing hard and playing well.
"When it does change, they're going to get rewarded and it will pay off somewhere along the line."
Notes: Ladd's assists gave him 302 career points and extended his points streak to six games, tying a career-high. He has four goals and eight assists in this streak. ... Jets centre Bryan Little played his 400th NHL game and had one assist to keep on a five-game points streak with one goal and eight assists. ... Wheeler is also on a five-game points run with three goals and seven assists. ... Staal's pair of assists gives him six points, all assists, in his last six games.