Pierre-Luc Dubois gave the Jets a 1-0 lead 50 seconds into the second period when he tipped in a Nate Schmidt point shot.
Jacob Peterson tied it 1-1 at 10:46 after Alexander Radulov fed him at the side of an open net.
"I know when [Radulov] has the puck, he's going to find me," Peterson said. "I just try to go to the net, and I know good things happen if I go there."
Tyler Seguin gave Dallas a 2-1 lead 56 seconds later at 11:42 off a cross-ice pass from Gurianov to finish a 3-on-1.
"I think that was the game we expected," Winnipeg coach Dave Lowry said. "We expected a fast, physical game. There wasn't a lot of big hits, but it was a heavy game. I thought we did a really good job of defending, managing the game. I thought we got ourselves into a little bit of trouble just by not getting pucks in deep, and we fueled their transition game, allowed them to get some momentum. But I thought we had some good answers."
Jansen Harkins tied it 2-2 at 16:21 with a wrist shot after a touch pass by Cole Perfetti at the top of the slot.
"I think we were pretty resilient all night just sticking with it," Harkins said. "Obviously you want to squeak out one at the end there. It's just a [lousy] way to lose."
Benn put the Stars in front 3-2 at 12:47 of the third when his redirection trickled through the five-hole of Hellebuyck.
"Every win from here on out is big for this group," said Benn, the Dallas captain. "We need to catch a lot of teams in front of us and try to separate ourselves from teams below us."