Elias Lindholm and Blake Coleman scored, Johnny Gaudreau had two assists, and Markstrom made 24 saves for the Flames (0-1-1).
"We've just got to get in front of the goalie and bare down on our chances," Gaudreau said. "We could've had three, four, five goals tonight if we find the net there. We've got to put the puck in the net."
Rakell tied it 2-2 at 12:55 of the third period, shooting blocker side on Markstrom from the high slot after receiving a cross-ice pass from Adam Henrique.
"We were lucky that it was a one-goal game for such a long time, and honestly when we got that tying goal, it gave the whole group some energy," Rakell said. "I think we had some good chances in the last period there [that] also gave us some confidence going into overtime. I thought we did a good job having the puck possession for most of the overtime, and then obviously 'Terrs' and 'Drys' made a great play on that winning goal."
Coleman, who was making his Calgary debut after he was suspended for the opener, made it 1-0 at 7:43 of the first period. He shot under Gibson's arm from the hashmarks on a breakaway after taking a pass from Gaudreau.
"It's obviously a good start," Coleman said. "I was excited. I had my daughter in the stands. That's kind of where my head went, honestly. She doesn't come to all the games. She's kind of been my good-luck charm. It's a fun thing we have. But from the hockey side of it it's another game, another goal that you're just trying to help your team win. I would've liked to bury another couple chances tonight, but we just couldn't get them to fall."