Jake Sanderson redeemed himself for an earlier mistake by tying the game, 3-3, for Ottawa (6-5-1) with 2:49 remaining with a shot from the top of the faceoff circle. Devin Cooley, who made 35 saves, had little chance as MacKenzie Weegar fell into him.
The Flames (2-8-2) benefitted from a Sanderson giveaway with Nazem Kadri and Jonathan Huberdeau playing a give-and-go before Kadri beat Linus Ullmark, who stopped 27 shots, at 8:16 of the third.
Artem Zub made it 2-2 at 2:36 of the third with a blast from just inside the blue line that beat a screened Cooley.
Despite a number of good chances, the Senators still found themselves trailing 2-1 after 40 minutes.
Cooley stopped Jordan Spence and made a couple big saves on Sanderson.
The Flames jumped out to a 2-1 first-period lead thanks to a pair of power-play goals.
Yegor Sharangovich opened the scoring at 5:51 beating Ullmark high glove side.
Ottawa tied the game less than two minutes later when Shane Pintoâ€s shot kicked out to Lars Eller at the side of the net for a short-handed goal.
With the Flames on the power play, Ullmark lost sight of the puck and Matt Coronato was able to get his stick on the loose puck in the crease and pick up his third of the season to regain the lead with 4:07 left in the first.
Senators: The Senators penalty kill continues to be an issue. Ottawa gave up two more power-play goals on four chances to Calgary.
Flames: The Flames got off to a solid start and capitalized on its opportunities early in the game.
With the game in overtime, Cooley made a save on Dylan Cozens from in close.
Senators: Head to Montreal to take on the Canadiens on Saturday.
Flames: Travel to Nashville to face the Predators on Saturday.
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