Monahan scored the 10th overtime goal of his career -- which ties Washington's Alex Ovechkin for the most in the NHL since the start of the 2013-14 season, Monahan's rookie campaign. It also was his eighth game-winning goal of the season, which is tops in the league.
The clubs will meet again Tuesday in Chicago in the second half of a home-and-home series. The Flames won the first meeting of the season 4-3 in overtime on New Year's Eve.
The winner at 59 seconds of overtime capped an entertaining see-saw clash at the Scotiabank Saddledome.
Vinnie Hinostroza doubled the lead early in the second period with a power-play tally. It was another beautiful setup by Kane, who collected his 499th career assist.
To their credit, the Flames didn't pack it in despite their recent woes and the deficit. Matt Stajan put the hosts on the board by converting on a breakaway with a shot that went just inside the far post behind Chicago goalie Jeff Glass at 5:56 of the middle period.
Less than seven minutes later, Johnny Gaudreau netted his first goal in eight games. He found space among a collection of defenders as he one-timed a shot from the circle for a 2-2 tie.
Anthony Duclair scored on a breakaway to again put Chicago ahead at 14:13 of the second period, but Michael Frolik knotted the affair with 10:10 minutes remaining in regulation.
Smith stopped 25 shots for the Flames, who were mired in a 0-2-4 slump that followed a seven-game winning streak.
Glass made 35 saves for the Blackhawks, who are on a 2-4-2 slide.
With his two helpers, Kane has 19 goals and 43 points in 36 career games against the Flames.
--Field Level Media