Branko Radivojevic also scored for the Wild, who won their fourth game in five outings. Harding got his first win of the season in his first start of the season.
It was the second straight listless performance from the Oilers since essentially giving up the playoff pursuit following the trade of Smyth to the New York Islanders.
Minnesota moved a point ahead of Calgary for seventh place in the Western Conference and 12 points ahead of the Oilers. Minnesota head coach Jacques Lemaire is glad to have more distance between the two teams than they did just five days ago.
"I thought the game we won at home against the Oilers on Sunday was even bigger than this one," he said. "They are all big, but if they had won that one it would have put them five points back of us. What is great about this one is it gives us some breathing room now."
Lemaire credited Harding for the poise he has shown the last two games with the Wild missing their regular goaltending tandem.
"The chances that they got, he was just great on them," he said. "They had the opportunities to score goals and get going, but he was there to make the big saves. It's a good thing because we don't have nobody else."
Harding was happy to have made the most of his opportunity.
"It's an unbelievable feeling right now," he said. "When I get home tonight it will hit a lot harder. I'm just enjoying the moment right now."
The Oilers have now lost three in a row and look a far cry from the squad that made it all the way to Game 7 of the Stanley Cup Finals last season. Edmonton head coach Craig MacTavish says the Oilers are struggling.
"There is just nothing right with our game right now," he said. "We have to find a way to be better than that. The starting point is to eliminate the five-star bonehead blunders.
"There has been a sense of futility the last two nights. It's frustrating to be in the situation we are in right now. It is going to be hard to battle through it mentally."
Oilers forward Raffi Torres says the only thing they can do at the moment is go out there and play the game.
"We can't be hiding out there," he said. "We can't crawl under the ice. We have to keep pitching away at it."
Minnesota started the scoring 11:23 into the first period when Martin Skoula sent Demitra in all alone. Demitra went to the backhand and beat Oilers starter Dwayne Roloson glove-side for his 20th of the season.
The Wild went ahead 2-0 on a two-man advantage with just under four minutes remaining in the first. Gaborik and Demitra worked the give-and-go down deep before Gaborik scored his 21st past Roloson.
Minnesota continued to put the Oilers on their heels early in the second as Edmonton defenseman Matt Greene wiped out, allowing a Wild two-on-one. Roloson got a piece of Mark Parrish's original shot, but the puck landed on the goal line, where Radivojevic was able to tap it in to put the Wild ahead 3-0.
Jussi Markkanen replaced Roloson in the Oilers net to start the third. But it didn't make much difference. Gaborik picked off a puck at the Oiler blue line and scored his second of the night on the breakaway. Demitra added his second goal on the power play with under four minutes to go.
Harding faced an Oilers two-man advantage for the final 1:50 to preserve his shutout.
- Harding came in during the second period of Wednesday's game against Calgary to replace Niklas Backstrom, who left the game with a lower body injury. Backstrom had been on a tear for the Wild since replacing starter Manny Fernandez, who is out with a knee injury.
- Thursday marked the Minnesota debut of forward Dominic Moore. He had six goals and 15 points in 59 games for the Penguins this season and led Pittsburgh in face-off wins.
- Defenseman Ladislav Smid and forward Petr Nedved returned from injuries to suit up for the Oilers, who lost Marty Reasoner to a right shoulder after a first period hit from Derek Boogaard.