Kane completed his fifth career regular-season hat trick and first since March 2017 by scoring into an empty net with 26.9 seconds left. He leads the Blackhawks with 20 goals and 47 points, and has five goals and five assists during a six-game point streak.
''It's always nice to produce,'' Kane said. ''It was fun with both (Saad) and me on the ice at the same time.
''We were trying to play hockey and make the right play, and hopefully one of us finished it off.''
Minnesota outshot Chicago 48-20 and the 24-year-old Delia, who appeared in just his fourth NHL game, drew as much postgame praise as Kane.
''Shots were a little bit misleading, I think, but they had their chances,'' Blackhawks coach Jeremy Colliton said. ''We got the lead but they really pushed.
''We had a little trouble getting out of the D-zone, but Delia was excellent. And we had some guys make some plays.''
''Our margin for error isn't very high right now,'' Staal said. ''We're not scoring enough to make some of the mistakes we're making.''
''We have a lot of Grade-A chances and we're not putting them in and we're not getting the save when we need to get the save,'' coach Bruce Boudreau said. ''It's not a good combination.''
Chicago went 2 for 4 on the power play, scoring more than one goal with the man advantage for the first time this season.
Kane opened the scoring 4:02 into the first. Although he was covered by Parise in the left circle, Kane batted in Gustafsson's cross-ice feed before Dubnyk could slide across the crease.
Parise tied it on a rebound with five minutes left in the first period, two seconds after a penalty to Chicago's Brendan Perlini expired. Minnesota tested Delia with a flurry of tough chances during the power play. As the man advantage lapsed, Delia stopped Staal's backhand stuff attempt, but Parise slid in a loose puck.
Saad put Chicago back in front 23 seconds into the second period on a shot from the slot. Toews' pass from behind the net bounced off Jason Zucker's stick and deflected to Saad, who ended a six-game goal drought.
Kane's second goal, a power-play score off a faceoff 3 1/2 minutes later, made it 3-1. Toews pulled the draw to Gustafsson at the left point, and he fed Kane in the right circle for a one-timer over Dubnyk's glove.
That prompted Boudreau to replace Dubnyk with Stalock.
''I hate pulling goalies,'' Boudreau said. ''I just didn't think he was seeing the puck well.''
Delia was sharp the rest of the way as the Blackhawks reverted to a close checking game and limited rebounds and mistakes.
Saad's second goal, a power-play score at 12:17 of the third, gave Chicago some insurance. After Stalock misplayed a loose puck, Alex DeBrincat intercepted it and fed Saad, who scored from the slot.
Boudreau pulled Stalock for an extra attacker with 3:42 left, and Staal scored on a rebound from a pileup with 50.3 seconds remaining to cut it to 4-2.
Kane completed his hat trick into an empty net on a shot from center ice.
NOTES: Parise was hit under the left eye by the stick of Chicago's Duncan Keith early in the second period. The Wild's leading scorer dropped to the ice but skated to the bench and returned a few minutes later. ... Dubnyk played in his 260th game for the Wild, tying the 32-year-old with Manny Fernandez for second-most by a Wild goalie. ... Minnesota star D Matt Dumba missed his fourth game with a torn right pectoral muscle. He had surgery this week and is expected to miss three months. ... Chicago C Marcus Kruger sat out his fourth game with a concussion. ... Wild forward Joel Eriksson Ek, a healthy scratch for the second straight game and third time this season, will be sent to AHL Iowa once the NHL's holiday roster freeze ends Friday.
Wild: At Winnipeg on Saturday.
Blackhawks: At Colorado on Saturday.
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