Kirill Kaprizov scored for the Wild in the second round. Marc-Andre Fleury stopped Chicago's Jonathan Toews and Patrick Kane in the shootout to help give Minnesota coach Dean Evason his 100th NHL victory.
Matt Boldy scored twice in regulation for Minnesota and rookie Mason Shaw had his first NHL goal. Fleury made 23 saves.
Jake McCabe, Andreas Athanasiou and Toews scored for Chicago in regulation.
Minnesota had the only shots in overtime, with Chicago goalie Alex Stalock stopping Joel Eriksson Ek with a brilliant toe save on the doorstop. Stalock stopped 32 shots.
Minnesota forward Ryan Hartman was injured in a scuffle with Jarred Tinordi in the second period, and didn't play the final 34 minutes. He went off favoring his right shoulder. The Wild called it an upper-body injury.
SETH JONES SIDELINED
The hard shot Chicago defenseman Seth Jones blocked Saturday night will cost him three to four weeks. X-rays Sunday confirmed a broken right thumb on the shot by Buffalo's Jeff Skinner in a 4-3 loss to the Sabres.
Wild: Host Montreal on Tuesday night.
Blackhawks: Host New York Islanders on Tuesday night.