Stafford scored the only goal in a four-round shootout and had a goal in regulation, and Myers had two assists and played a strong game on defense in the Winnipeg Jets' 5-4 victory against the Detroit Red Wings on at Joe Louis Arena.
Stafford and Myers were acquired earlier in the week in a trade with the Buffalo Sabres. This was their second game with the Jets.
"I just want to keep contributing any way I can," said Stafford, who snapped a shot past the left arm of Detroit goaltender Jimmy Howard in the shootout.
Winnipeg coach Paul Maurice said any player new to a team wants to make an immediate impact.
"They were welcomed and now they feel like they put something in the bank," Maurice said. "You want to make plays and help your new team win and they did that."
Chris Thorburn, Blake Wheeler and Andrew Ladd also scored in regulation for Winnipeg (29-19-10). Dustin Byfuglien had two assists and Hutchinson made 25 saves through 65 minutes. He also stopped Stephen Weiss in the final round of the shootout for the win.
Hutchinson has stopped all 11 shootout attempts he's faced in his career.
"He's a good fighter in net." Maurice said. "That would be his trait. He fights for the puck."
Pavel Datsyuk had two goals and an assist, Darren Helm scored a goal and had an assist, and Niklas Kronwall scored a power-play goal for Detroit (31-13-10). Tomas Tatar had two assists. Howard, in his first start in more than a month, made 34 saves.
"I just thought our lack of ability to take care of the puck in the offensive zone in the second half of the game hurt us," Red Wings coach Mike Babcock said.
Datsyuk tied it at 4-4 by beating Hutchinson with a wrist shot from the slot with 6:33 remaining in regulation.
Ladd's power-play goal 4:38 into the third period gave Winnipeg a 4-3 lead. He put a wrist shot from the inside top of the left circle past Howard for his 19th goal.
The Jets scored twice in a span of 2:44 in the second period to tie the game 3-3.
Wheeler put the rebound of Myers' shot into an open net from the crease at 7:04 to make it 3-2. It was Wheeler's 16th goal.
Myers jumped into the play from his defensive position and cut in off right wing to get off his shot.
"I love the chance to jump into the play, and the way these guys play the game, I'm going to get the chance to do that," Myers said.
Maurice said that goal changed the momentum of the game. He also talked about what Myers brings to the Jets.
"You get down 3-1, it's nice to have someone other than Dustin (Byfuglien)," Maurice said "[Jacob Trouba] can jump in the odd time, but it's nice to have another guy who can jump into the play."
Stafford's first goal for Winnipeg tied it at 9:48. It appeared that Howard had Stafford's backhand shot from the bottom of the right circle. But the puck somehow slipped through and trickled into the net. It was the 10th goal of the season for Stafford.
The Red Wings took the lead earlier in the middle period with two goals in 3:35.
Helm's power-play goal at the two-minute mark made it 2-1. He backhanded a loose puck past Hutchinson for his 12th of the season. Datsyuk was credited with his 16th goal at 5:55 when Helm's shot from the right circle hit his shoulder and went past Hutchinson. It was Datsyuk's first goal in 10 games.
Thorburn opened the scoring 2:36 into the game when he redirected Trouba's shot from the left point past Howard for his second goal of the season. It was the first shot Howard saw in his first start after missing 11 games with a partially torn groin muscle.
"Sometimes I felt a little ahead of the game and sometimes I felt a little behind the play. It'll come," Howard said.
Kronwall tied it with a 5-on-3 power-play goal with 3:06 left in the period. He beat Hutchinson with a one-timer from the high slot off a pass from Henrik Zetterberg. It was Kronwall's sixth goal and came with Wheeler and Ladd serving penalties taken at 15:16; Wheeler was called for boarding and Ladd for holding.