The Kings were 5-0 this season in shootouts and Backstrom had lost eight straight shootouts before Tuesday night.
Johnson was the Kings' second shooter, and he made a brilliant deke to get Backstrom flat on his belly.
"From the bench, all I saw was open net," Wild coach Todd Richards said.
Backstrom somehow made a kick save with his right skate, one of three he made in the shootout, and Pierre-Marc Bouchard followed with the game winner to lift the Wild to a 1-0 victory over the Kings.
"He had me beat so I tried just to get something up there and got lucky," Backstrom said. "It hit my skate. You need those every now and then."
Bouchard beat Jonathan Bernier with a nifty little backhand through the five-hole and Backstrom also stopped Anze Kopitar and Dustin Brown to help the Wild get a much-needed two points in the airtight Western Conference.
Bernier was even better than Backstrom during regulation and overtime, making several point-blank saves for the Kings, who had their three-game winning streak snapped in the first of a 10-game road trip.
Backstrom was rarely challenged during his third shutout of the season, but was superb in the shootout. He poke-checked the puck off the stick of Kopitar to start the shootout and capped it off with a blocker save against Brown.
"I just tried to wait him out," Johnson said of his chance. "I tried to get him down and thought I had him waited out. He stuck his pad up and I hit him in the toe. I've got to tip my hat to him. He made a great save."
Bernier earned his first shutout of the season and stopped Marty Havlat to start the shootout before Bouchard beat him.
"He made a nice move," said Bernier, who had 25 saves. "I don't know if that's what he wanted to do at first. ... Obviously I'd like to get that one back."
Both teams looked rusty in their first game back from the six-day All-Star break.
The lack of offense should come as no surprise for two teams who have struggled on that end of the ice all season. The Wild started the night tied for the second-fewest goals in the West while only four teams had scored fewer goals than Los Angeles.
After a slow start to the season led to questions about Richards' job security, the Wild have moved back into the playoff hunt. They have won five of their past six games, and their latest victory over them 57 points for the season, one ahead of the Kings, and ninth place in the conference.
The Kings were one of the more disappointing teams in the first half of the season, unable to capitalize on the momentum gained from their first trip to the playoffs since 2002. They tied a franchise record with 46 victories last season.
Los Angeles lost 10 of 12 home games during a horrible skid that started at the end of December and dragged well into January before finally showing signs of steadying itself with a three-game winning streak going into the All-Star break.
With the Grammy Awards and the NBA All-Star game scheduled for Staples Center in Los Angeles, the Kings will spend the next three weeks crisscrossing North America in a trip that could define their season.
"The most important thing, obviously, is to win, but you want to play good," coach Terry Murray said. "You want to give yourself every opportunity to win the game. I thought we did that."
Wild LW Andrew Brunette played in his 1,000th career game. Since 1998, no player has played in more games than the Wild's beloved "Bruno." He received a standing ovation in the first period. ... Twins manager Ron Gardenhire was in attendance. He planned to play goalie in an instructional segment on Fox Sports North's postgame show. ... The Wild played their first 0-0 regulation home game since March 27, 2007.