With the game tied 3-3, Kane's unassisted goal at 9:12 of the third period came after Flames goaltender Jonas Hiller turned the puck over behind his net.
After straying out of his net to stop the puck, Hiller's attempted backhand pass to Dennis Wideman took a sharp carom off the end boards allowing Kane to intercept it. After Kane tucked the puck through the skates of Sven Baertschi, he slipped a quick shot through Hiller's pads.
It was the seventh goal of the season for Kane, who appears to be heating up for Chicago after scoring just four times in the club's first 16 games.
Calgary had a chance to tie it when Johnny Gaudreau drew a penalty with 3:32 left in the game. However, the Flames — having scored twice already on the NHL's No. 1 ranked penalty killing team — could not score despite Curtis Glencross having a couple of chances in front.
Adam Clendening, with his first NHL goal, Daniel Carcillo and Brent Seabrook also scored for Chicago (11-7-1). With the circus having arrived at the United Center, the Blackhawks kicked off a six-game road trip, which continues on Saturday night in Edmonton.
Paul Byron, Wideman and Sean Monahan scored for Calgary (12-7-2). The Flames had entered the night red hot, having won seven of their last nine.
Corey Crawford made 24 saves for the win, improving to 8-4-1.
Hiller had 18 saves. His record falls to 9-5-1.
Chicago took its second lead of the night when Seabrook got the puck in the slot and slapped a shot past Hiller at 10:52 of the second period.
However, the resilient Flames answered right back less than two minutes later.
Glencross set up a wide-open Monahan at the side of the Chicago net and he buried his eighth of the year on a one-timer — all of his goals coming in the last 12 games.
In their first matchup earlier this season, Chicago — despite losing 2-1 — outshot the Flames 50-18 and early Thursday night it looked like this game would follow a similar script.
Halfway through the second period, the Blackhawks led 2-0 and were outshooting Calgary 10-3.
However, an interference penalty on Chicago's Marcus Kruger turned around the game's momentum.
Late in an effective power play with sustained pressure, the Flames capitalized with Byron knocking in a rebound after Crawford made a pad stop off Josh Jooris.
As the goal was going in, Niklas Hjalmarsson tripped Monahan on the slot and as a result, Calgary went right back onto the power play and the Flames scored again with Wideman's slapshot from the blue-line finding the back of the net at the 14:38 mark of the period.
It was the eighth goal of the year for Wideman, who only had four all last season. That leads NHL defencemen.
The two power-play goals in a span of 54 seconds equals the number of goals Chicago's No. 1 ranked penalty killing unit had surrendered in the previous 14 games.
Picking up an assist on the goal was impressive rookie Markus Granlund, who has five points in his last three games and nine on the season in 10 games.
Chicago opened the scoring four minutes into the game when Glendening, in his second NHL shift, scored on a power play. His shot from the blue-line beat Hiller just inside the goal post.
Glendening was recalled from Rockford (AHL) on Tuesday when Chicago lost defenceman Trevor van Riemsdyk to a serious knee injury, which will require surgery and will sideline the rookie for 3-4 months.
Chicago made it 2-0 at 7:12 when Carcillo notched his second of the season.
Notes: The Blackhawks and Flames are two of the NHL's best third period teams. Calgary outscoring opponents 27-13 and Chicago outscoring teams 22-7... Returning to the Calgary line-up after missing eight games with a concussion was LW Michael Ferland, who got hurt in his NHL debut on Oct. 31... Also absent from the line-up for Chicago was C Andrew Shaw (upper body). Shaw is considered day-to-day. He was replaced by Jeremy Morin... Seabrook was playing in career game No. 700.