It was the seventh overtime game the Hurricanes have played this season and the first one they have won.
Cam Ward made 22 saves to get the victory and end Carolina's two-game skid. It was the first time since Oct. 18, in the sixth game of the season, that Ward had given up fewer than two goals.
Andreas Nodl gave Carolina the lead 2:33 into the game but Filip Kuba tied it with 2:45 to go in the opening period.
Craig Anderson stopped 36 shots in defeat. The Senators had won their previous three games.