"It's really good for me and my confidence right now," said Khudobin, who was summoned from Houston of the AHL earlier this month after Backstrom went down with a hip-flexor strain.
Khudobin was less than four minutes away from a second consecutive shutout before a power-play goal by Magnus Paajarvi.
"No," Khudobin said when asked if he was disappointed to lose the shutout. "The W is better for me."
The Wild got goals by Matt Cullen, Brent Burns, Pierre-Marc Bouchard and Andrew Brunette to improve to 31-20-9 all-time against the Oilers, the most wins they've had against any opponent.
Khudobin also blanked Vancouver 4-0 on Sunday. At the other end of the ice, Nikolai Khabibulin allowed goals to Cullen and Burns before the game was 3 1/2 minutes old on the way to losing his ninth consecutive start.
"It's nice to get that lead early, particularly on the road," said Cullen, who opened the scoring at 1:39. "Especially when you look back on it. We didn't have a particularly good first period. We didn't play as well as we'd like, but you come in after the period leading 2-0 and it's something to feel good about."
The only good news for the Oilers is they ended a drought that had seen them go 11 games without a power-play goal when Paajarvi scored with 3:46 remaining.
"We were not good in the beginning," Paajarvi said. "We can't let that happen. We tend to play good in the second and third (periods). We've got to play 60 minutes."
Adding injury to insult as the Wild took a 3-0 lead in the season series, the Oilers also lost forward Hemsky in the second period with a concussion.
Cullen put the Wild up 1-0 when he backhanded his own rebound past Khabibulin just 1:39 into the game. Burns made it 2-0 on Minnesota's fourth shot, sifting a wrist shot from the blue line through traffic past Khabibulin at 3:25.
While a portion of a capacity crowd jeered each of the four saves Khabibulin made the rest of the period, Edmonton's power play also fed the discontent, running its streak to 0-for-40 by managing just two shots on its two tries with a man advantage.
Edmonton got four more cracks at Minnesota's 12th-ranked penalty killing in the second period, including a 5-on-3 advantage for 1:40 with Antti Miettinen and Greg Zanon both off for tripping -- and produced just one shot on goal.
"That was a huge turning point in the game," Minnesota coach Todd Richards said of killing the 5-on-3. "I thought we did a good job. It was a long 5-on-3, too, and I thought we did a good job limiting their chances, at least their good looks at the net."
The Oilers got nothing for their efforts, running their skein of frustration to 0-for-44, as Khudobin stopped all 12 shots he faced in the period to get the Wild to the second intermission still up 2-0.
Hemsky, who has already missed 13 games with a groin strain, sustained the concussion late in the first period. He came out for the second period, took one shift and left the bench for the dressing room.
Bouchard tucked the puck inside the right post at 10:03 of the third period after a giveaway for a 3-0 lead, and Brunette made it 4-0 at 12:07, just five seconds into a power play.