Kovalchuk scored his 33rd goal in the second period and his 34th (empty net) with three seconds left in the contest. He also assisted on two third period goals from Rich Peverley and one by Todd White.
It was his first five-point contest this season.
Kari Lehtonen made 32 saves on 35 shots for the Thrashers, who trailed, 3-1, before their explosion.
They had lost two of three.
Carolina got one goal each from Tuomo Ruutu, Sergei Samsonov and Anton Babchuk (power play).
Cam Ward was beaten four times on 31 shots for the Hurricanes, who kept pace with Buffalo in the race battle for the eighth and final playoff seed in the Eastern Conference.
The Sabres lost 2-0 to the New York Islanders. Atlanta and Buffalo both have 69 points.
Celebrity Families of 2014 [PHOTOS]