With time running out in regulation, Sergei Samsonov kept the puck in the Atlanta zone at the right point. Ian White kept it alive along the boards and made a behind-the-back pass to Cole, who quickly blasted a one-timer past Ondrej Pavelec.
Jiri Tlusty and Joe Corvo also scored for Carolina.
Cam Ward turned aside 41-of-43 shots as the Hurricanes downed the Thrashers for a fifth straight time.
Andrew Ladd notched both Atlanta goals.
Pavelec made 14 saves for the Thrashers, who fell two points behind the Hurricanes for the eighth and final playoff spot in the Eastern Conference.