Florida's Tim Thomas and Buffalo's Jhonas Enroth staged a goaltending duel in a meeting of the bottom two teams from the Atlantic Division, but the contest was ultimately decided by Boyes.
Boyes deflected a shot from Tom Gilbert past Enroth to tie it with 10:44 left in regulation and then produced the only shootout goal.
Enroth had stopped 36 shots in regulation and overtime as well as the first two shootout attempts before giving up the game-winner.
Buffalo's goal came from Jamie McBain 5:13 into the contest.
Thomas finished with 24 saves.
The Sabres came up short in their bid to win back-to-back games for just the second time this season.
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