The shot from Myers sailed over Vokoun's left shoulder and brought the Sabres their third straight victory.
The teams traded goals in both the second and third periods and the game appeared headed to a shootout before Myers scored for the seventh time this season.
Mike Weber put Buffalo in front midway through the second only to have Steve Bernier tie it on the power play with 1:22 to go in the period.
Thomas Vanek again gave the Sabres the lead 8:59 into the third, but Martin Reasoner forged a 2-2 deadlock 64 seconds later.
Ryan Miller made 24 saves to get the win. Vokoun stopped 24 shots in what was Florida's fifth loss in six games.
Swim Week Miami Beach 2014 [PHOTOS]