Paul tied it 1-1 at 4:31 of the second with a weak wrist shot from the right point that deflected off Tony DeAngelo and appeared to catch Andersen off guard.
Formenton redirected a point shot from Victor Mete to give the Senators a 2-1 lead at 5:50 of the third period, but Niederreiter jammed in a rebound in the crease to tie it 2-2 with 3:22 remaining.
"That was a huge goal by Nino," Andersen said. "Even though they scored early in the third, I thought we came out really well and pushed them and tried the whole period to tie it up and force overtime. It was a nice win, of course."
It was the first time the Hurricanes played in an empty arena this season. Ontario's current COVID-19 restrictions do not allow for fans at sporting events.
"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."
Senators forward Josh Norris left in the first period with an upper-body injury after awkwardly crashing into the boards on a hit by Svechnikov. He will be reevaluated Friday, but coach D.J. Smith said he is "hopeful" the forward won't be out long term.
Norris is the sixth forward currently injured for Ottawa, joining Colin White (shoulder), Shane Pinto (upper body), Connor Brown (broken jaw), Drake Batherson (ankle) and Dylan Gambrell (upper body). Defenseman Nikita Zaitsev also did not play because of a lower-body injury.
"I think you can see that everyone is stepping up for each other," Stutzle said. "We're working really hard. Everyone is hitting really hard and playing good defensively, and I think that helps a lot. With Drake and Josh [out], we're missing a lot, and we have Pinto and White out. We literally have all our top centers out right now, but I mean, everyone is stepping up."
NOTES: Svechnikov had his five-game multipoint streak end. … Stepan is two points shy of 500 in the NHL. … Formenton has scored five points (two goals, three assists) during a five-game point streak.