Carolina's Nino Niederreiter scored with just about three minutes remaining in regulation to force overtime, and Derek Stepan had the team's other goal.
Carolina coach Rod Brind'Amour called goalie Frederik Andersen, who made 37 saves, the star of the night.
''He was the difference in the game,'' Brind'Amour said. ''He came up huge a lot and just allowed us to hang in there and finally get the tie and get a chance to win.''
Ottawa's Brady Tkachuk had a breakaway in overtime and the Senators had a 49-second power play after Tim Stutzle drew a hooking penalty but came up short both times.
''We had every chance,'' Senators coach D.J. Smith said. ''Against a team like this you want to win. I thought we played hard.''
Alex Formenton and Nick Paul scored for the Senators, and Matt Murray made 27 saves.
Josh Norris went hard into the boards late in the first period, took his time before getting up and did not return. Smith said the Senators will have an update Friday and remain hopeful it's nothing serious.
Ottawa was playing without leading scorer Drake Batherson and Dylan Gambrell, who were both injured Tuesday.
''I thought we played hard you know,'' Paul said. ''It's not easy losing (Batherson) and (Norris) (Thursday) and Gambrell so, there's spots to be taken and there's opportunity and guys stepped up.''
The Hurricanes opened the scoring two minutes into the second as Stepan tipped a shot in front to beat Murray. But two minutes later, the Senators tied the game when Paul made what looked like a harmless shot on goal, but it hit Tony DeAngelo on the way and fooled Andersen.
Formenton scored the go-ahead goal for the Senators early in the third. He tipped a Victor Mete shot in for his ninth of the season. Formenton now has 11 points in his last 10 games (four goals, seven assists).
Due to COVID-19 restrictions, the Senators continue to play without fans - something the Hurricanes are not used to.
''You don't want to make excuses, but it's tough playing a game here,'' Brind'Amour said. ''It feels like it's practice, the environment, especially when we're just now getting used to the electricity being back in the building.
''It's the same for both teams, but it was obvious that was a big factor in the game.''
The Senators announced Batherson will likely miss a couple months, if not more after suffering a high ankle sprain Tuesday against Buffalo. ... Ottawa signed defenseman Nick Holden to a one-year $1.3-million contract extension Thursday. He could have been an unrestricted free agent at the end of the season.
Hurricanes: Host New Jersey on Saturday.
Senators: Host Anaheim on Saturday.
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