Trailing 3-2 entering the final period, Carolina began its rally when Eric Staal scored his second goal of the contest on a wrist shot from the left circle with 9 1/2 minutes to play.
Then with 1:22 left, LaRose tallied after Winnipeg couldn't clear the zone and the Hurricanes hung on to post their third straight win.
Jussi Jokinen added a goal and two assists for the winners.
Cam Ward stopped 30 shots for Carolina, which pulled to within five points of the eighth and final Eastern Conference playoff spot.
Ondrej Pavelec managed 31 saves as Winnipeg remained two points out of the East's final playoff berth.