New Jersey rallied to a 2-2 deadlock when Karel Rachunek scored his third goal this season at 15:25 of the second and Mike Mottau's third at 6:16 of the third period created an overtime.
Buffalo also got a goal from Henrik Tallinder in the second round of the shootout, while New Jersey failed to score on either of its shootout chances.
Ryan Miller stopped 24 of 26 shots in regulation for the Sabres, who have won five of their last six contests.
Martin Brodeur stopped 20 of 22 shots in regulation and was beaten twice in the shootout for the Devils, whose three-game road winning streak ended.
Swim Week Miami Beach 2014 [PHOTOS]