Brind'Amour was a Hurricanes assistant for seven seasons before being named May 8, 2018, to replace Bill Peters.
"It's a great win. The guys played hard," Brind'Amour said. "We made a lot of mistakes but we're covering up for them."
WATCH: [All Hurricanes vs. Blue Jackets highlights]
Sebastian Aho and Micheal Ferland each had a goal and an assist, Jordan Martinook scored, and Curtis McElhinney made 31 saves for Carolina in his first game after being claimed off waivers from the Toronto Maple Leafs on Monday to replace injured Scott Darling. McElhinney played for Columbus from 2013-17.
"I'm always grateful at any time to play in this league," McElhinney said. "For Carolina to give that is tremendous, but it's been tough. It's been a hard week for me and my family. I've got people in Toronto right now and I'm not sure when they're going to make it down."
Brandon Dubinsky scored, and Sergei Bobrovsky made 32 saves for the Blue Jackets in their home opener.
"They're a fast team," Columbus coach John Tortorella said. "They don't give you much space. You have to give them credit how they check. They check hard.
"When we had some really good chances in the second period, [McElhinney] made some key saves."
The Hurricanes took a 1-0 lead at 1:43 of the first period on a shot from between the circles by Martinook. Andrei Svechnikov, the No. 2 pick in the 2018 NHL Draft, got the assist for his first NHL point.
Dubinsky made it 1-1 at 12:58, putting in a rebound over McElhinney's pad.
"They're good. They're fast. They jammed us up a bit along the walls," Dubinsky said.