Zemgus Girgensons forced overtime by scoring the tying goal with 3:54 left in regulation. Jhonas Enroth made 26 saves through overtime and then sealed the victory by stopping Ondrej Palat and Ryan Callahan in the shootout.
The Sabres (9-14-2) have won six of seven since a 3-13-2 start.
Palat scored for the Lightning (17-6-3), who had won four straight. Evgeni Nabokov stopped 21 shots before allowing goals on both shootout attempts he faced.
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