Babchuk took a cross-ice pass from Justin Williams and beat Atlanta goalkeeper Kari Lehtonen with a nifty backhand shot for his first goal of the season. Two of Atlanta's three losses have come against Carolina, including its last loss on Oct. 13. Since then Atlanta had won four straight.
The Hurricanes fell behind 1-0 as Eric Boulton scored 3:14 into the game when he netted a tip-in. Carolina rallied and scored the next three goals to take a 3-1 lead at the end of the first period as Eric Staal, Scott Walker and Andrew Hutchinson scored.
Atlanta tied the game in the second period, as the Thrashers took 22 shots.
Jon Sim stole a pass from Carolina's Bret Hedican at the Hurricanes' blue line and scored at 11:31.
Then at 17:21, Scott Mellanby scored on a tip-in from the right post as the puck bounced over Cam Ward's pads.
Ryan Bayda's first goal of the season didn't stand up for the Hurricanes, whose 4-3 lead in the third period was short-lived.
Ilya Kovalchuk, who extended his goal-scoring streak to three games, tied the game at 4-all when he deflected a shot in the slot from Vitaly Vishnevski with 11:39 left.
Kovalchuk has scored five goals in the last three games. Walker hit the post from point-blank range with three minutes left, missing a chance to give Carolina the lead.
Atlanta's Marian Hossa took a hooking penalty with just over two minutes left in regulation but Carolina, which was 1-for-6 on the power play, was not able to convert.
Atlanta was 0-of-4 on the power play. Ward finished with 32 saves against 36 shots, while Lehtonen stopped 33 of 38 shots.
Notes: Carolina RW Scott Walker reached 300 career points with a goal and an assist. Atlanta LW Kovalchuk has scored a point in five straight games.