In the extra session, Chicago's Jonathan Toews obtained the puck and skated into the Calgary zone on the right side of the ice. He made a stop-and-start move to get past a defender in the right circle, then flew across the crease, drawing Flames goaltender Miikka Kiprusoff in his direction.
Toews sent the puck back toward the slot past a sprawled Kiprusoff, and Keith was there to backhand the disc into the open net to end the game.
Dave Bolland and Patrick Kane each scored once for the Blackhawks, who had won the previous five games during their current string of victories in regulation. Chicago is averaging 4.66 goals per game during the streak, thanks in part to a 9-2 pasting of Edmonton on Tuesday.
Nikolai Khabibulin stopped 32 shots in the win for Chicago.
Rene Bourque had a goal and assisted on David Moss' tally for Calgary, which had won two in a row. Kiprusoff turned aside 28 shots in the loss.
Bourque had the only goal of the first period, but Bolland lit the lamp just 1:08 into the middle frame to knot the game at 1-1.
Kane's 15th goal of the season, a power-play score, edged Chicago in front a little over five minutes after Bolland's tally, though Moss provided the equalizer at the 8:32 mark of the second.
The goaltenders were strong in the third period, with each making several key saves. Kane almost notched the game-winner on a clear breakaway with 4 1/2 minutes to play, but Kiprusoff stoned the offering as the game went to overtime.