Eriksson Ek cut it to 2-1 seven seconds into a power play, at 19:30.
"We thought Greenway, 'Ek' and [Foligno] really drove us tonight," Wild coach Dean Evason said.
Zuccarello passed to Kaprizov in the slot on the power play to tie the game 2-2 at 10:45 of the third period, but Borgstrom put the Blackhawks ahead 3-2 at 12:03.
"Yeah, it's tough," Borgstrom said. "I feel like we needed this, and we played really well. It could have gone either way."
NOTES:Wild defenseman Jared Spurgeon had two assists in 23:06 after missing seven games with a lower-body injury. … It was Lankinen's first start since Dec. 18. … Kaprizov extended his personal point streak to eight games (seven goals, eight assists). … Zuccarello has four consecutive multipoint games for the first time in his NHL career and has scored 14 points (three goals, 11 assists) in his NHL career-best eight-game point streak. … Fiala (six goals, three assists) extended his point streak to eight games. … Zuccarello, Greenway and Alex Goligoski each had two assists for Minnesota. … Blackhawks forward Patrick Kane had his nine-game point streak end (two goals, nine assists). … It was Borgstrom's second multigoal game in the NHL and first since March 2, 2019 with the Florida Panthers in a 4-3 loss to the Carolina Hurricanes.