The Panthers fell behind 2-1 early in the final period, but rallied thanks to constant pressure in a 37-shot barrage on Dallas goaltender Kari Lehtonen.
Aleksandr Barkov tied it with 9:28 remaining and Goc then took a feed from Tomas Fleischmann before beating Lehtonen from short range.
Goc added an empty-net goal with 1:30 to go.
Tim Thomas picked up the victory by making 25 saves. Thomas, a two-time winner of the Vezina Trophy as the NHL's top goaltender, made his debut with Florida after spending the first eight years of his career with Boston.
The Dallas goals came from Alex Chiasson and Brenden Dillon.