Patrick Sharp and Brian Bickell also scored for the Blackhawks, who have won just two of six.
Jordan Eberle had the lone goal for the Oilers, who have lost five of six and 19 of 23.
The Blackhawks had the first prolonged pressure of the game midway through the first period, and it paid off as Jonathan Toews passed to a hard-charging Sharp, who scored his 27th goal.
The Blackhawks went up 2-0 five minutes into the second as Taylor Hall's errant pass to the point was taken up ice on a breakaway by Bickell, who beat Devan Dubnyk with a backhand deke.
Dubnyk was coming off his first career shutout on Monday at Nashville.
Chicago's Corey Crawford was barely tested in the first 40 minutes. His biggest stops came in the closing seconds off a pair of shots in tight from Hall.
The Blackhawks took a three-goal lead four minutes into the third period on their sixth power play. Tomas Kopecky made a nice backhand feed from behind the goal line to Kane, who snapped the puck into the net to make it 3-0.
Eberle ruined Crawford's shutout bid with 3:40 left in the game as he scored on the rebound of Jim Vandermeer's point shot.
Kane put the game away with an empty-net goal with 43 seconds left.
Oilers coach Tom Renney wasn't at the game because he was traveling to Cranbrook, British Columbia, to attend his father's funeral. Assistant coach Ralph Krueger ran the bench against Chicago and will lead the Oilers again against Ottawa on Saturday.
Notes: Chicago traded forward Jack Skille to the Florida Panthers before the game. Skille and prospects Hugh Jessiman and David Pacan were dealt for forward Michael Frolik and highly touted Czech goalie Alexander Salak from the Swedish Elite League. ... It was the fourth and final meeting of the season between the teams. Edmonton won two of the first three. ... Blackhawks D Niklas Hjalmarsson didn't practice Tuesday after blocking four shots against Calgary on Monday, but was in the lineup on Edmonton. ... Oilers D Tom Gilbert, who left the pervious game after taking a knee to the head, returned to action. ... Oilers forward Andrew Cogliano played in his 300th NHL game.