Tomas Holmstrom added a goal and an assist and Drew Miller also scored for Detroit, which at least temporarily moved into the eighth and final Western Conference playoff spot. Jimmy Howard made 21 saves.
The Red Wings have sometimes started slowly this season and have blown a few third-period leads.
"I thought we got started on time and played 60 minutes," Detroit coach Mike Babcock said.
The Red Wings lost 4-2 to the Calgary Flames on Tuesday night at Joe Louis Arena. They let a 2-1 third-period lead slip away in that game.
"We thought about that and made sure we didn't make any mistakes," Franzen said. "We always had three guys back."
"They were digging for the puck, going in there with speed," Wild captain Mikko Koivu said. "And we were going the other way."
Detroit led 3-1 after the first period.
Franzen opened the scoring 2:25 into the game when his slap shot from the top of the right circle bounced in off of Harding's arm for Franzen's sixth goal.
Holmstrom's power-play goal made it 2-0 9:19 into the first period when his slap shot from the left point deflected in off the skate of Minnesota defenseman Nick Schultz. It was Holmstrom's 19th goal. Zetterberg got his 19th just 56 seconds later when he scored from the lip of the crease.
Detroit moved usual third-line center Valtteri Filppula up to the second line to play left wing along with Zetterberg at center and right winger Dan Cleary in an attempt to get Zetterberg going. Jason Williams moved down to the third line with Todd Bertuzzi and Miller, who switched from a wing to center. Apparently, it worked
"I always put pressure on myself," Zetterberg said. "I try not to care what other people are saying. You just have to believe in yourself and keep going and do the best you can."
Ebbett put the Wild on the board with only 11 seconds left in the opening period when his pass from the corner deflected in off the skate of Detroit defenseman Brad Stuart's skate for Ebbett's seventh goal.
"They came out and smacked us early," Minnesota center Kyle Brodziak said. "Jumped out to a 3-0 lead. Such a good team to try and come back on."
Miller's short-handed goal with 7:02 left in the second period made it 4-1. The rebound of Filppula's shot from the lip of the cease bounced in off Miller's body for his eighth goal and first short-handed effort of his career.
"It hit him in the shoulder, bounced and hit me in the stomach," Miller said. "It looked like it was going to hit my stick in my hands but it was too late. Luckily, it went off my stomach and went in."
Franzen scored his second with 5:17 left.
Minnesota goalie Niklas Backstrom tweaked his groin during the morning skate. Wild coach Todd Richards said he was day to day. ... Minnesota right winger Cal Clutterbuck returned after missing one game with a lower body injury. ... Ebbett played at the University of Michigan. ... Wild left winger Guillaume Latendresse was helped off the ice after being accidentally hit in the back of the neck by Brian Rafalski's stick as Latendresse reached for the puck off a faceoff 8:33 into the second period. Ralfalski received a high-sticking penalty. Latendresse didn't return. Richards said he was taken to the hospital just as a precaution. Richards didn't think it was serious.
Copyright by STATS LLC and The Associated Press
DETROIT - MARCH 11: A view from above at the before an NHL game with the Minnesota Wild vs. the Detroit Red Wings...