Brodie scored at 2:26 of the extra session Tuesday night to lead Flames to a 5-4 win over the slumping Blackhawks, whose overtime record fell to 0-6 this season.
"Overtime's been a sore spot," said Chicago coach Joel Quenneville, baffled by his team's inability to play well in OT. "I think we've got enough assets in there. In overtime, we've got to find a way to make it happen."
Brodie picked up a rebound in front of Chicago goalie Corey Crawford before scoring a wraparound goal.
"It's always nice winning, especially against a team like that," Brodie said.
"There was a battle on the red-line and Stempy won the battle and gave a pass to Mony," Brodie explained. "Mony made a good play cutting to the middle and got a shot off. Crawford sort of slid out of the net from the shot. I just tried to wrap it around back out front and it ended up going in."
Mikael Backlund scored twice for the Flames (19-27-7), who won three straight games for the first time this season.
"There was a lot of emotions out there, a lot of chances back and forth," Backlund said. "These are fun games to play. I'm sure the coaches didn't think that, but I enjoyed the game."
"They're a hard-working team so we expected them to work hard," Kane said. "They always seem to give us a tough game in this building. We had to be ready for it. I thought we did a good job fighting back. It was just a few too many mistakes."
Neither of the starting goalies played particularly well and both were replaced in net by their respective head coaches.
Antti Raanta drew the start in net for Chicago, but was pulled after he stopped just 11 of 15 shots he faced through 1 1/2 periods of play. Crawford entered and stopped 13 consecutive shots before giving up Brodie's OT goal.
The Flames held a pair of one-goal leads in the first period before the Blackhawks responded both times to tie up the game 2 after 20 minutes.
Calgary jumped out to a quick start as captain Mark Giordano rang a shot off the post 37 seconds into the game. Backlund then scored his 10th goal of the season at 1:13 of the first.
Backlund took a pass from linemate Lee Stempniak and shook off a check from Chicago defenseman Niklas Hjalmarsson before backhanding a shot that sneaked through Raanta's legs.
The Blackhawks evened the score at 5:53 when Kane converted a nice backhand pass from Kris Versteeg from behind the Calgary net.
The Flames regained their one-goal lead at 11:34 when Bouma's weak wrist shot hit Raanta in the shoulder before bouncing up and over the Chicago goalie and into the net.
Once again, the Hawks drew even on a goal by Hossa with 3:25 remaining in the opening period. Patrick Sharp appeared to score the goal, but his stick hit Hossa's, which directed the puck into the net behind Berra, who made a great pad save to stop the initial shot taken by Jonathan Toews.
David Jones made a nice play to set up Stajan for his ninth goal of the season at 3:21 of the second before Backlund converted a feed from Stempniak for a short-handed marker at 10:25 to put the Flames up 4-2.
The Hawks pulled within one when Smith's long wrist shot bounced off of Berra's catching glove and into the net. Hossa then tied the game at 4 when he swatted a rebound past Berrra at 17:33 of the second while Chicago was killing off a penalty.
In overtime, Crawford stopped a shot from the slot by Calgary forward Sean Monahan. Brodie then picked up the rebound and scored a wrap-around goal.
The Flames are in the middle of a five-game homestand, which equals their season high. They also played five straight games at home from Dec. 23 to Jan. 3 when they went 1-4. ... The Flames will also host the San Jose Sharks on Thursday and the Minnesota Wild on Saturday. ... It was Backlund's first multi-goal game since Oct. 21, 2010, when he scored both times for Calgary during a 4-2 loss to the Red Wings in Detroit. ... With an assist on Backlund's second goal, Giordano extended his point-scoring streak to seven games, a career high.