Josh Harding made 29 saves for Minnesota.
Zetterberg has been impressive from the start of the season. He increased his totals to 21 goals and 19 assists and has at least a point in all but three of the Red Wings' 28 games.
"Your best players have to be your best players," Detroit coach Mike Babcock said. "He and Pav (Datsyuk) come to play every night.
Hasek, meanwhile, has struggled early in the season. But this was his second consecutive win after losing three straight starts.
"I believe I can continue to play like this," Hasek said. "I can feel it more in my heart and my stomach. I am talking more, you can hear me on the ice. I bang my stick more on the ice and that's what I need to be doing to keep myself in the game and play on the best level."
Hasek even was assessed a tripping penalty with 2:19 left.
The Wild's Marian Gaborik had a breakaway on Hasek from just outside the Red Wings' blue line. And as Hasek often does when he sees a shooter on a breakaway with his head down, he charged out of his net to try and knock the puck away. Hasek then slid out and did knock it away. But in the process, he also flipped Gaborik skates over head to the ice.
"I got there first to the puck and I don't think it's supposed to be a penalty," Hasek said. "His head was down, I didn't go after him, I went directly for the puck. I got the puck first, then I hit him. I hit him with my legs, but I have to protect myself also. I cannot go into him with my shoulders."
The Red Wings broke it open with three goals in a span of 4:19 in the second period.
Zetterberg's second goal of the game, which came short-handed, made it 2-0 at 5:31 of the middle period. He picked up a loose puck in front of the Minnesota net, made a move and put a shot past Harding.
Hudler made it 3-0 just 50 seconds later when he scored on a one-timer from the bottom of the left circle, for his seventh goal, while a penalty was being called on the Wild and Hasek on the bench for a sixth attacker. Franzen added a power-play goal at 9:50, when he jammed in a rebound for his second goal.
"In the second, we had a couple of bad breaks," said Harding.
Zetterberg completed the hat trick 41 seconds into the third period on a one-time slap shot from the right circle.
"When you get one, you want to get two. When you get two, you want to get three," he said said. "When you have a chance (for a hat trick) you give it a little extra."
The entire line of Zetterberg, Datsyuk and Tomas Holmstrom, who had an assist, had the puck in the Minnesota zone all night long.
"He's (Zetterberg) just great... That whole line" Wild coach Jacques Lemaire said. "Just look at their stats."
Datsyuk has 11 goals and 23 assists and Holmstrom 13 goals and 14 assists.
"Them and that (Sidney) Crosby line (with Pittsburgh), they're right up there," Harding said.
Zetterberg gave Detroit a 1-0 lead with 2:17 left in the opening period when he put in a rebound from the bottom of the left circle.
- Detroit C Kris Draper (knee), and LW Kirk Maltby (back) missed the game.
- Minnesota Kurtis Foster returned after missing four games with a facial fracture.
- Wild RW Mark Parrish returned after missing three games with hip injury.