Mikael Samuelsson and Ville Leino also scored, and Marian Hossa had two assists to help the Red Wings win their sixth straight. The team was without Tomas Holmstrom (hernia surgery), Johan Franzen (hand) and Brad Stuart (back).
"We've got other guys who are pretty good too," Samuelsson said.
Osgood has struggled this season despite his 18-4-6 record. But he made big saves when he needed to.
"It's more mental than anything else," Osgood said. "I'm going out there now without the weight of the world on my shoulders. As an athlete you have high expectations for yourself."
Brent Burns and Mikko Koivu scored for Minnesota, and Antti Miettinen had two assists. Josh Harding made 39 saves.
Wild coach Jacques Lemaire agreed with Samuelsson.
"They have about nine players who can do things constantly," Lemaire said.
Hudler gave Detroit a 2-1 lead with 9:38 left in the second period, beating Harding with a one-time shot from the bottom of the right circle for his 18th goal after a give and go with Hossa. Draper then scored on a slap shot from the top of the left circle with 8:48 left - also off a pass from Hossa.
"It's always a little tough playing against those guys," Harding said. "They have a lot of skill."
Leino made it 4-1 with 2:45 left in the second when he scored on a wraparound.
"In the second we took over and we played creative," Hossa said. "We got the three-goal lead. In the third period, we just controlled the game."
Koivu picked up a short-handed goal with 9:35 left, cutting in off the right wing and stuffing a shot past Osgood. It was Koivu's 16th goal.
Samuelsson opened the scoring 9:26 into the game when he put in a puck from the crease after Brett Lebda's shot trickled through Harding's pads. It was Samuelsson's 15th goal.
Burns' power-play goal tied it for Minnesota with 4:29 remaining in the first period. He scored on a one-time shot from the right circle for his eighth goal. The Wild had a two-man advantage and the goal came 1:14 after Hossa and Datsyuk were both called for hooking with the Red Wings' already short-handed.
Notes: Minnesota LW Derek Boogaard, the team's enforcer, was a healthy scratch. ... Lebda left the game with a back injury after taking a hit behind the Detroit net against the boards by the Wild's Cal Clutterbuck early in the second period. Lebda didn't return and won't make the trip to Columbus for Friday night's game. He's day-to-day. ... Datsyuk's nine-game points streak ended.
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