Drysdale tapped in a pass from Troy Terry at 3:26 of overtime for the winner.
“Troy kind of did all the work, made a great fake, great curl and drag and then slipped it through the guy, right on my tape, back door,” Drysdale said.
It was the first OT winner for the 19-year-old from Toronto.
“Awesome,” Drysdale said. “It’s obviously really exciting, especially being back here in Canada. It’s nice, even though the fans were cheering against us, the energy was real good. It’s nice to have fans back in the building.”
Cam Fowler and Rickard Rakell also scored for the Ducks, who started a four-game trip with a victory.
“We bent a fair amount, but we didn’t break,” Anaheim coach Dallas Eakins said.
Anaheim goaltender John Gibson made 41 saves. He sat out Friday’s loss to Minnesota with a lower-body-injury.
“To come out with this win, not only just being my first goal in overtime, this was a really big win for our group and it’ll set us up nicely moving forward into this road trip,” Drysdale said.
Blake Coleman scored in his debut with the Flames, and Elias Lindholm added a goal. Johnny Gaudreau had two assists, and Jacob Markstrom stopped 24 shots.
Calgary lost a second straight game putting 40-plus shots on the opposition’s net. The Flames generated 47 in a 5-2 season-opening loss in Edmonton on Saturday.
“We have 40 shots in both games, but we’ve got to get someone in front of the net,” Gaudreau said. “We’ve got to take the goalie’s eyes away and find a way to score some greasy goals.”
With Ducks defenseman Josh Manson serving high-sticking penalty with just under four minutes to go, Calgary’s power play couldn’t produce a go-ahead goal.
Rakell, on a give-and-go with Adam Henrique, pulled Anaheim even at 12:55 of the third period. Henrique fed an unchecked Rakell in the high slot. Rakell scored on a shot over Markstrom’s right pad.
Calgary led 2-1 at 3:52 of the second period on Lindholm’s second goal in as many games. He collected a cross-ice pass from Gaudreau and threaded a shot between Gibson’s pads from the faceoff dot.
Fowler pulled Anaheim even with a power-play goal at 15:54 of the opening period. He took a drop pass from Kevin Shattenkirk and scored past Markstrom’s right pad.
Coleman scored the first goal at 7:43 of the first. Gaudreau tapped the puck up to the winger in the neutral zone. Coleman fired a wrist shot under Gibson’s left arm.
NOTES: Calgary is without a captain. The Flames are rotating assistant captaincies among four players: Tkachuk, Mikael Backlund, Sean Monahan and Chris Tanev. … Former Flames head coach Geoff Ward, now a Ducks assistant coach, returned to the Saddledome for the first time since Calgary fired him March 4. … Mason McTavish, who at age 18 is Anaheim’s youngest-ever goal scorer, didn’t play Monday’s third period because of a lower-body injury.
Ducks: At Edmonton on Tuesday, the second of a four-game week.
Flames: Start a five-game trip at Detroit on Thursday.