Justin Williams, Ray Whitney, Eric Belanger and Chad LaRose also scored, and Kevyn Adams had an empty-net goal to help Carolina improve to 9-3-2 in its last 14 games.
John LeClair and Mark Recchi had second-period goals for Pittsburgh. The Penguins have lost five straight and have been outshot 179-101 during that slide.
Erik Cole had two assists in his first game against the player who nearly ended his career. Cole broke his neck last March when Pittsburgh's Brooks Orpik rammed him into the boards, causing an injury that cost the Carolina forward three months.
Cam Ward, coming off his first career regular-season shutout two nights earlier against Washington, made 18 saves and improved to 4-1-0 in five career starts against the Penguins.
Jocelyn Thibault stopped 24 shots in his second start of the season.
Williams scored Carolina's first goal with a two-man advantage, tapping a loose puck past Thibault at 12:51. Whitney made it 2-0 5 minutes later, taking a pass from Cole and beating Thibault with a wrist shot.
Brind'Amour gave the Hurricanes a three-goal lead when he scored on the power play 1:29 into the second period, one-timing a pass from Eric Staal to make it 3-0.
The Penguins scored twice later in the second to make it a one-goal game. LeClair started the rally when he trickled a shot past Ward at 3:18, and Recchi pulled Pittsburgh to 3-2 with a slap shot from the left circle at 16:42.
But Belanger restored Carolina's two-goal lead midway through the third period when he came down the left side and beat Thibault with a wrist shot.
Adams and LaRose scored short-handed goals 51 seconds apart late in the third.
The Hurricanes finished 2-for-13 on the power play and kept the Penguins scoreless on seven chances with the man advantage.
Tensions were high at the start. Orpik was booed lustily nearly every time he touched the puck, and then things got chippy about seven minutes in. Carolina's Mike Commodore and Pittsburgh's Chris Thorburn traded punches, with each player drawing five-minute penalties for fighting.
Notes: Cole's two assists gave him 101 for his career. ... Carolina improved to 2-0 this season against the Penguins. The Hurricanes won 5-1 on Oct. 14. ... Cole has four goals and five assists in his last four games. The Hurricanes won three of those and lost the fourth in a shootout at New Jersey. ... Recchi played his first game at the RBC Center since helping Carolina win the Stanley Cup. He signed with the Penguins during the off-season. ... Hurricanes D Tim Gleason (shoulder) missed his sixth straight game. D Niclas Wallin also did not play. ... Scratched for Pittsburgh were forwards Ronald Petrovicky and Andre Roy, and D Eric Cairns.