The Blackhawks, who eliminated Minnesota from the play-offs for the third consecutive season, will face either Anaheim or Calgary in the West final, with the Ducks leading the Flames 2-1 in their series.
Defenseman Brent Seabrook gave Chicago the lead midway through the first period and Andrew Shaw doubled their advantage 3:28 into the second.
The Wild pulled a goal back three minutes later through Erik Huala but the Blackhawks opened up a three-goal cushion in the third, with goals from Patrick Kane and a short-handed effort from Marian Hossa.
Minnesota made the Blackhawks sweat in the closing stages as goals from Jason Pominville and Nino Niederreiter in the last three minutes narrowed the deficit to 4-3.
But Chicago held on to complete the four-game sweep during a series in which the Wild never led.
Goaltender Corey Crawford made 34 saves to help play his part in the win, stopping 124 of the 131 shots he faced.
Chicago did suffer an injury blow though, after defenseman Michal Rozsival lost his balance and his ankle bent back awkwardly as he fell.
In the night???s other NHL play-off game, Carey Price stopped 22 shots, Max Pacioretty scored a goal and provided two assists, as Montreal Canadiens beat Tampa Bay Lightning??6-2 to keep their second-round play-off series alive as they reduced the deficit to 3-1.
Pacioretty and Andrei Markov scored in the first period as the Canadiens avoided a sweep with their first victory in nine games this year against the Lightning.
Tampa Bay goaltender Ben Bishop allowed three goals on 14 shots before he was pulled a little over five minutes into the second period.
Bishop had 30 saves in Tampa Bay’s 2-1 victory on Wednesday night.
Game five takes place on Saturday night in Montreal, where Tampa Bay won the first two games of the series.