Rod Brind'Amour, Ray Whitney and Josef Vasicek each had a goal and an assist in the big period that LaRose capped with a goal against Devils backup Scott Clemmensen.
Scott Walker and Tim Gleason also scored for the defending Stanley Cup champions, who lost a 3-2 decision to New Jersey on Thursday in a game in which Brodeur stopped 38 of 40 shots.
John Grahame faced 10 shots in the opening 40 minutes as Carolina built a 5-1 lead. He finished with 18 saves as the Hurricanes beat New Jersey for the first time in four games and remained in an Eastern Conference playoff spot with nine games left in the regular season.
David Clarkson, who was called up from the minors this week because of groin injuries to Patrik Elias and John Madden, scored his first NHL goal and set up another by Travis Zajac for the Devils. New Jersey has lost five in a row at home.
Coming into the game, LaRose had four career goals in 119 games, including a game winner on his first NHL goal against Brodeur in December 2005.
LaRose faked a shot from the top of the left circle, skated to the dot and beat Brodeur with a low shot that seemed to fool the goaltender at 4:48 of the first period.
The Hurricanes blew the game open early in the second period, with Vasicek, Whitney and Brind'Amour scoring in less than a five-minute span.
Vasicek deflected a Gleason shot over Brodeur's shoulder. Whitney capped a 3-2 by taking a pass from Brind'Amour and scoring his 28th goal. Brind'Amour sent Brodeur to the bench for only the second time this season with a shoulder-height deflection of Glen Wesley shot.
The play was reviewed and Brodeur left after it was ruled a goal.
Clarkson cut the lead to 4-1 with a shot from the left circle but LaRose scored from the right circle with 3:02 left in the period to end any hopes of a Devils' comeback.
NOTES: Wesley got his 400th career assist on LaRose's first goal. ...Hurricanes D Niclas Wallin appeared to hurt his right knee late in the first period but came back and played. ...The win was only the Hurricanes' 11th in 25 games. ...The Hurricanes have allowed one power play goal in 13 games, killing off 50-of-51 chances. ...