Jan Rutta and Richard Panik also scored for the Blackhawks. Chicago (2-0-0) has outscored opponents 15-2 this season and has opened with back-to-back wins for the first time since the 2014-15 campaign.
Sonny Milano scored the lone goal for the Blue Jackets. Columbus (1-1-0) dropped its third consecutive contest at the United Center, where it has not won since March 27, 2015.
Blackhawks goaltender Corey Crawford stopped 32 of 33 shots in the victory.
Blue Jackets goaltender Joonas Korpisalo turned aside 24 of 29 shots in his season debut.
Kane opened the scoring 1:33 after the opening faceoff to give Chicago a 1-0 lead. He snapped a rising wrist shot from the right circle for his second goal in as many games.
Later in the first period, Chicago pulled ahead 2-0 when Saad punched in a loose puck in front of the net. The goal marked the fourth of the season for Saad, who netted a hat trick in the season opener.
A one-timer by Toews increased Chicago's lead to 3-0 with 9:46 remaining in the second period.
Columbus answered 31 seconds later to cut the deficit to 3-1. Nick Foligno crashed toward the crease, and Milano tapped in his second goal in as many nights.
Chicago made it 4-1 on Rutta's first career NHL goal with 7:09 left in the second period. Kane set up the score with a hard backhand pass that zipped across the slot.
Panik finished the scoring with 5:55 remaining in the third period.
Blackhawks center Nick Schmaltz absorbed a hard hit in the first period and did not return.
NOTES: The Blackhawks played a video tribute in the first period for Blue Jackets LW Artemi Panarin, who spent the previous two seasons in Chicago before he was traded for LW Brandon Saad this summer. ... Blue Jackets G Sergei Bobrovsky had the night off after posting his 20th career shutout one day earlier. ... Blackhawks C Tommy Wingels made his team debut. The 29-year-old played for San Jose and Ottawa before signing with his hometown team. ... Columbus D Scott Harrington and RW Josh Anderson were healthy scratches. ... The Blackhawks held a moment of silence for Pierre Pilote, who died last month at age 85. Pilote served as team captain from 1961 to 1968.