Heatley tied it at 3-3 less than five minutes into the second period and hit an empty net with 1:47 left to make it 6-3. Rheaume scored both of his goals on breakaways, including Atlanta's fifth with 6:32 to play.
Ilya Kovalchuk and Chris Herperger also tallied for the Thrashers, who entered the night with a league-low four points. Their wins have come in the last three games, both on the road.
The Sabres built a 2-0 lead in the opening 11:19 but had their winless streak extended to eight (0-6-2). They had not gone eight games without a win since October 1993.
Notable deaths of 2014 [PHOTOS]