Kaprizov cut it to 2-1 with a wrist shot from the top of the left face-off circle at 8:23 of the third period.
Knyzhov, a defenseman playing his 38th NHL game, extended the lead to 3-1 when he scored from the left circle off a feed from Erik Karlsson at 10:58.
"There's not much to say, that was just a great play by [Hertl and Karlsson]," Knyzhov said. "I wasn't expecting that pass, but that was awesome. I give a lot of credit to [Karlsson]."
Zuccarello scored with 13 seconds remaining make it 3-2, and Evander Kane scored into an empty net with one second left for the 4-2 final.
The Sharks defeated the Wild 4-3 in the shootout here Monday.
"There's a lot of season left," Wild captain Jared Spurgeon said. "You can't just look at these two games and start pouting. We didn't play our best the first two periods. I thought we responded in the third. But we got two games left on this road trip starting tomorrow (at the Vegas Golden Knights) and we can turn this thing around real quick."
NOTES: Kaprizov leads the Wild with 12 goals. …With an assist, Fiala extended his point streak to three games (one goal, three assists). …The Sharks won a fourth straight game at home. … Kane had six shots on goal, three hits and one blocked shot. … Burns is one assist from 500 in the NHL. He can become the 30th defenseman in NHL history to reach the mark, and the 19th with at least 200 goals, 500 assists and 700 points.