Lowry scored his fourth goal at 4:41 of the second to put Winnipeg ahead 2-1. He crashed the Dallas net and jabbed a loose puck under Niemi.
Klingberg scored his seventh goal at 14:41 of the second. On a delayed Winnipeg penalty, Klingberg finished a 3-on-0 rush, taking a pass from Demers and flipping the puck over Hellebuyck.
Fiddler scored 2:11 later, snapping a low shot past Hellebuyck for his seventh goal and a 3-2 Stars lead.
"They're a good enough team that if you give them 20 minutes of room, 10 minutes of room, they can make you bleed for it, and we did," Jets coach Paul Maurice said.
Stafford struggled to explain Winnipeg's second-period lull.
"There's not an easy answer to that," Stafford said. "They just were a little harder on the puck than us, won a few more battles. Turnovers in our end, some sloppy play."
Seguin scored his 27th goal, on the power play, at 2:49 of the third period to make it 4-2.