Drayson Bowman scored twice and recorded an assist for the Hurricanes. Goaltender Brian Boucher made 21 saves and recorded his first win of the season.
Kyle Brodziak had a goal and two assists for Minnesota. Nick Johnson and Erik Christensen also scored for the Wild, who have lost eight of nine games.
Trailing 3-2, Carolina quickly changed the direction of the game in the third period. With the teams playing 4-on-4, Bowman made a perfect pass to a streaking Sutter for a breakaway. Sutter made a nice move and his backhand beat Minnesota's Matt Hackett on the stick side to tie it at 7:16 of the third.
Less than a minute later, Brent launched a shot from just inside the blue line that got past Hackett and gave the Hurricanes a 4-3 lead. The goal came just as a Minnesota penalty expired.
Chad LaRose added an empty-net goal at 18:45.
The comeback allowed Boucher (1-4-1), out of action since early December, to win for the first time for the Hurricanes. Boucher, a veteran who previously won 119 NHL games for six different teams, missed 36 games earlier this season with a lower body injury.
Bowman got credit for Carolina's second goal at 17:14 of the second period that cut the lead to 3-2. He passed the puck to Sutter in the slot, but the puck went off of the skate of Minnesota's Devin Setoguchi and into the net before Sutter could touch it.
Bowman opened his second two-goal game of the season by picking off a bad pass from Clayton Stoner and firing the puck past Hackett at 1:02 of the first period.
Minnesota was in control for much of the first two-plus periods.
Johnson gave Minnesota a 2-1 lead at 12:33 of the second period when he knocked his own rebound up and over Boucher. Three minutes later, Brodziak made a perfect centering pass to a streaking Christensen — who scored for the third time in three games — and the Wild led 3-1.
With three points, Brodizak tied his career high of 37 points in a season, set a year ago with Minnesota. The center has also recorded five points in the past four games for the Wild.
Hackett made 29 saves for Minnesota.
Notes: Minnesota C Mikko Koivu was not activated despite practicing each of the past two days. The Wild's captain has now missed 14 games with a shoulder injury. ... Wild G Niklas Backstrom has now missed seven games in a row with a groin injury. ... Carolina coach Kirk Muller started D Justin Faulk against the Wild. Faulk was last on the Xcel Energy Center ice last April when he helped Minnesota-Duluth win the NCAA title. ... Carolina is in the midst of playing 10 of 12 games on the road. ... Tom Gilbert, acquired by the Wild from Edmonton at the trade deadline, recorded his second point for Minnesota with a first-period assist. He now has two points in nine games.