Atlanta has won three straight overall and three in a row over the Devils, including two victories in five days. The Thrashers have six consecutive victories over New Jersey at Philips Arena.
Zach Parise scored two goals for the Devils.
Atlanta's first power-play opportunity had just expired when Hnidy gave the Thrashers a 3-2 lead 6:42 into the second. Hnidy beat Martin Brodeur over the left shoulder with a wrister from outside the top of the right circle.
Kozlov's 13th goal came with 11:46 remaining after he took Marian Hossa's pass from behind the net and skated across the bottom of the slot.
Ilya Kovalchuk's 20th goal, an empty-netter, ended the scoring with 26.7 seconds remaining.