Stafford scored the only shootout goal Saturday night to lift the Jets to a 5-4 victory over the Detroit Red Wings and snap a five-game road skid.
His wrister got past Detroit's Jimmy Howard in the fourth round of the tiebreaker and Michael Hutchinson stopped Stephen Weiss on the ensuing attempt to seal Winnipeg's first road victory since Jan. 16.
"It was a weak goal, but we'll take it," said Stafford said after his team erased a two-goal deficit.
"To come back and win, that just shows the kind of character that we have."
The Jets began the game three points ahead of Calgary in the conference wild card standings.
Tyler Myers, like Stafford, playing his second game with the Jets after arriving in a trade with Buffalo, added two assists.
"They were welcomed and now they feel like they put something in the bank," coach Paul Maurice said of the duo, who went scoreless in Thursday's 3-1 loss at Nashville. "You want to make plays and help your new team win and they did that."
Howard, who missed 11 games with a partially torn groin muscle, made 34 saves for Detroit in his first start since Jan. 6. The Jets' Hutchinson stopped 25.
Andrew Ladd also had a regulation goal for Winnipeg, which improved to 14-6-4 against Eastern Conference teams this season. Pavel Datsyuk had two goals for Detroit.
The loss ended Detroit's six-game home winning streak.
Howard was named an NHL All-Star but missed the game with the injury. He seemed a bit erratic in the second but said he expects to return to form soon.
"Sometimes I felt a little bit ahead of the play and sometimes I felt a little behind the play," he said after falling to 0-7 in shootouts this season.
Detroit coach Mike Babcock was pleased to see his goalie get plenty of work.
"It's probably good for Howie to see lots of rubber," he said. "That's good."
Ladd's power-play goal gave the Jets a 4-3 lead early in the third, but Datsyuk tied it with a wrist shot with 6:33 to play. Winnipeg's Mathieu Perreault had a great chance to end the game early in overtime but Howard stopped his breakaway shot.
The Jets got the game's first goal less than four minutes in after Chris Thorburn redirected Jacob Trouba's shot past Howard. Winnipeg drew matching minor penalties later in the period and Niklas Kronwall knotted the score with a power-play marker.
Detroit's Darren Helm backhanded a rebound early in the second and assisted on Datsyuk's first goal a few minutes later, but the Jets rallied to tie the game midway through. Blake Wheeler knocked in a rebound to halve the deficit and Stafford knotted the score when his shot dribbled out of Howard's grasp.
Red Wings defenceman Kyle Quincey was helped off the ice late in the third period after crashing into a corner but returned to action shortly after. He was assessed a roughing penalty at 2:50 of overtime but the Jets were unable to convert despite sending six shots at Howard in the extra five minutes.
"It was a huge kill for us," said Detroit coach Mike Babcock, who added he plans to start Howard on Monday when Atlantic Division foe Montreal comes to town.
Notes: The Red Wings had three goalies on the active roster Saturday but that could change soon. Petr Mrazek, who went 8-2 in Howard's absence, could be sent down to Grand Rapids of the AHL because Babcock said he'd rather the 23-year-old play regularly. . The goal was Stafford's first since coming to Winnipeg in the trade that sent Evander Kane and Zach Bagosian to Buffalo. . Detroit sent defenceman Jakub Kindl to Grand Rapids for a four-game conditioning stint.