Gaudreau, who finished with two assists, was playing his first game in Calgary since signing a seven-year, $68.25 million contract ($9.75 million average annual value) with Columbus on July 13.
"It'll probably be easier next time, but I'm sure I'll still get booed," said Gaudreau, who played his first eight NHL seasons with the Flames. "It'll be a lot easier. The first time back is a lot of emotions. [I was] a little nervous before the game started, but I was excited to be back. It was a lot of fun playing here."
Dillon Dube won it for Calgary at 2:25 of overtime with a one-timer from the top the right face-off circle on a 2-on-1. The rush began after Gaudreau lost control of the puck and fell down at the Flames blue line.
"It would've been better if we won it in 60 (minutes) there," Dube said. "It was a huge effort."