Buffalo won its third straight and climbed out of the cellar in the Northeast Division, a point in front of Montreal.
The Stars took a 2-0 lead 4:17 into the third period on a slap shot by Tomas Vincour, but Thomas Vanek produced a power-play goal less than a minute later to bring the Sabres within one.
Roy saved the game for Buffalo with his slap shot that beat Kari Lehtonen.
Each side delivered a goal in the first three rounds of the shootout and it continued until Gerbe lifted a backhander over Lehtonen. Dallas' Michael Ryder then missed the net with his attempt to give Buffalo the win.
Ryan Miller made 24 saves for the Sabres, who have won five of their last six. Lehtonen stopped 30 shots.
Swim Week Miami Beach 2014 [PHOTOS]