Suter's strike came with both teams short-handed 3:03 into the third. The 13-year veteran's dragging wrist shot from the right circle sailed just above Anton Forsberg's glove, with Mikko Koivu and Mikael Granlund assisting.
Jonas Brodin also had a goal for Minnesota (23-17-4), which snapped its two-game skid. Suter's goal was his sixth of the season and Brodin's was his fourth.
Brent Seabrook scored the lone goal for Chicago (21-16-6). It was Seabrook's first goal since the Blackhawks' opening-night 10-1 rout of Pittsburgh on Oct. 5.
The Blackhawks had won two straight.
The Wild were coming off a couple of tough losses, 7-2 at Colorado last Saturday and 3-2 in overtime versus Calgary on Tuesday.
Devan Dubnyk stopped 34 of 35 shots for Minnesota. Anton Forsberg made 25 saves for Chicago.
Seabrook tucked in a rebound of Michal Kempny's one-timer off Dubnyk's blocker with 7:36 remaining in the first period to put Chicago up 1-0. Nick Schmaltz, playing in his 100th NHL game, was credited with a secondary assist. Minnesota challenged the goal on the basis of offsides, but the call was upheld.
The Wild answered one period later when Brodin's slap shot deflected off a defender's stick past Forsberg with 10:02 to go in the second. Jason Zucker and Matt Dumba got the assists.
Minnesota's Nino Niederreiter missed his second straight game with a lower-body injury.
Chicago made waves on the trade front before the game, dealing Richard Panik and Laurent Dauphin to Arizona for Anthony Duclair and Adam Clendening.
Prior to puck drop, Chicago's Patrick Kane and Minnesota's Eric Staal were named NHL All-Stars for the seventh and fifth times, respectively.
The Blackhawks continue their six-game homestand Friday against Winnipeg, who then visit the Wild on Saturday.
--Field Level Media
Minnesota | Chicago | |
Jonas Brodin 1 | Points | Brent Seabrook 1 |
Jonas Brodin 1 | Goals | Brent Seabrook 1 |
Matt Dumba 1 | Assists | Michal Kempny 1 |
N/A | Power Play Goals | N/A |
N/A | Short Handed Goals | N/A |
Devan Dubnyk .971 | Save Percentage | Anton Forsberg .926 |
Devan Dubnyk 34 | Saves | Anton Forsberg 25 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Minnesota | 27 | 2 | 0-3 | 3-3 | 6 | 28 |
Chicago | 35 | 1 | 0-3 | 3-3 | 6 | 35 |