Brady Skjei and Jesperi Kotkaniemi each had a goal and an assist, Stefan Noesen had two assists, and Antti Raanta made 26 saves for the Hurricanes (50-18-9), who have won three in a row.
Carolina remained three points ahead of the New Jersey Devils for first place in the Metropolitan Division. New Jersey defeated the Pittsburgh Penguins 5-1 on Tuesday.
"It's a good thing to get a win and help the team get two points," Raanta said. "That's obviously the main goal for the rest of the way."
Claude Giroux and Brady Tkachuk scored, and Alex DeBrincat had two assists for the Senators (37-34-7), who have lost three straight and 10 of 14. Leevi Merilainen made 34 saves in his NHL debut.
Ottawa is six points behind the Florida Panthers and New York Islanders, who are tied for the first wild card into the Stanley Cup Playoffs from the Eastern Conference. Florida defeated the Buffalo Sabres 2-1 on Tuesday.
"I thought we stayed with it. We checked right with these guys," Senators coach D.J. Smith said. "You don't like the result in overtime, but to a man, those [defenseman] back there, especially those young kids, did a really nice job."
Kotkaniemi gave the Hurricanes a 1-0 lead at 1:50 of the first period, tipping in a one-timer by Skjei from the left point.
Skjei then pushed it to 2-0 at 15:58, scoring glove side when his wrist shot from between the circles deflected off the glove of Shane Pinto on a power play.
Skjei has an NHL career-high 18 goals this season, tying Dougie Hamilton (2018-19) for the most by a defenseman since the Hurricanes moved to Carolina for the 1997-98 season.
"I think I got pretty lucky on that one, I was shooting for the left side," Skjei said. "I feel like I have a pretty good shot, a pretty hard shot, but I think my accuracy this year has been up."