Mikko Koivu added a goal and two assists for the Wild, who have won three of four. Cal Clutterbuck picked up a goal while Owen Nolan and Andrew Brunette registered a pair of helpers each.
Niklas Backstrom stopped 40 shots for his 22nd win of the season.
Martin Havlat produced the lone goal for the Blackhawks, who have dropped two of three.
Nikolai Khabibulin dropped his second straight decision after allowing three goals on 25 shots.
Minnesota got the game's first goal just after the midway point of the first period when Koivu's shot from the slot deflected off a skate and zipped under the crossbar.
Zidlicky's blast from the point on the power play with 1:46 left gave the Wild a 2-0 lead, then he beat Khabibulin to the short side at the left post 5:53 into the second for a 3-0 Minnesota edge.
"The first I had a nice screen, and then a great pass from (Brunette)," said Zidlicky of his tallies. "Sometimes you shoot too much and nothing goes in, other times you get two shots and they both go in."
Havlat's goal at the midway point of regulation reduced Chicago's deficit to 3-1, but Backstrom closed the door from there, He made 17 stops over the middle 20 minutes to keep the visitors up by two.
The Hawks were granted a power play with 3:32 left in the contest and pulled Khabibulin for an extra attacker and 6-on-4 advantage, but Clutterbuck locked up the win with an empty-net score with 33.7 seconds remaining.
"We came out flat, and just didn't have any energy," said Hawks defenseman James Wisniewski. "They really wait for their opportunities and we played right into it."