Kaprizov and Eriksson Ek each had a goal and an assist, and Kaapo Kahkonen made 22 saves for Minnesota (34-14-5), which has won three of four.
The Wild remained one point behind the second-place Colorado Avalanche in the West. The Avalanche defeated the Los Angeles Kings 3-2 on Friday. The first-place Vegas Golden Knights, Avalanche, Wild and St. Louis Blues qualified for the Stanley Cup Playoffs from the eight-team division.
"We didn't like our game at all," Minnesota coach Dean Evason said. "We knew that they were going to play hard and that they were going to be good.
"… But for us, the good part is, if there is a good part, they said all the good things on the bench. We asked them if they got tired of hearing themselves say 'Get it in deep and don't turn it over' because that's how we feel. Hopefully we got it out of our system and we can go forward tomorrow [in the second of the back-to-back set]."
Adam Henrique, who missed the past six games in NHL COVID-19 protocol, had a goal and an assist, and John Gibson made 32 saves for Anaheim (17-30-8), which is in last place in the West.
"I mean, the standings are the standings. I think it's just important to finish out the year strong," Henrique said. "With guys in and out of the lineup, everybody has to have the mindset to finish the year off strong. Whether that's for personal goals or whatever, I think it's important."