Karlsson tied it 2-2 on a 2-on-1 rush with Evander Kane at 15:45 of the second period.
He gave San Jose a 3-2 lead at 4:11 of the third period with a slap shot from the point. It was Karlsson's first two-goal game since Dec. 19, 2017, for the Ottawa Senators against Minnesota.
"I think I'm going to shoot it if I get it in positions where I can shoot it," Karlsson said. "I got to shoot it a little bit more sometimes, but I think today, the first goal is a 2-on-1, I know I'm getting the pass, I'm just positioning myself to shoot it when I get it. The second one, same thing. There's no one really in front of me, and I get a pass down low and walk the line and have a good screen. So if I keep getting in situations like that, I'll shoot the puck."
Fiala tied it 3-3 at 9:48 when he scored on the rebound of a shot by Johansson.
"We passed up a lot of opportunities to shoot the puck," Wild coach Dean Evason said. "… So that's our main concern here tonight. But we thought we competed well."
Jared Spurgeon scored for Minnesota at 2:07 of overtime, but the goal was immediately waved off because he batted the puck out of the air with a high stick.
NOTES:It was the first shootout this season for the Wild. … Johansson has scored a goal in two straight games for the first time since Oct.7-9, 2019, for the Buffalo Sabres. … Talbot got the second assist on Johansson's goal, his first with Minnesota and the fourth of his NHL career. … Sharks forward Jeffery Viel had two hits in 7:28 in his NHL debut. He fought Wild forward Luke Johnson 2:57 into the game.