Scheifele gave the Jets a 1-0 lead with his 20th goal of the season at 1:58 of the first period. A loose puck fell to Cole Perfetti in the left face-off circle, and he backhanded it to Scheifele waiting alone at the doorstep.
Jansen Harkins made it 2-0 at 7:20, tipping Morrissey's slap shot from the point between Swayman's pads.
"They battled hard, so that's all you can ask," Winnipeg coach Rick Bowness said. "So, you'd like to see a few more shots on net, yeah. A little more pressure on their [end], yeah, but the guys did work hard, and again, [Boston's] the top team in the League, so we were right there with them."
NOTES: Morrissey's 11-game point streak (14 points; one goal, 13 assists) is tied with four others for second-longest in Jets/Atlanta Thrashers history; the longest is held by Patrik Laine (15 games in 2017-18). Colorado Avalanche defenseman Cale Makar had an assist in 13 straight last season. … It is Scheifele's eighth season with 20 goals, which ties him with Ilya Kovalchuk for most in Jets/Thrashers history.