Columbus came within one goal of its season high and reached five goals in a single contest for only the fourth time all season.
Umberger gave Columbus a 2-0 lead midway through the second period, boosted the Blue Jackets in front 3-1 late in the middle stanza and finished off the hat trick with 5:02 to play in the third.
Vinny Prospal and Mark Letestu also scored for the Blue Jackets, who have defeated Carolina in each of their last five meetings.
Steve Mason made 39 saves to get the win.
Carolina's playoff hopes took another hit against the worst team from the Western Conference. The Hurricanes slipped seven points out of the final playoff position with seven games to play.
Cam Ward allowed all five goals on 26 shots.