In the opener, Craig Smith and Derek Roy scored in a shootout to give Nashville a 2-1 victory.
In the second game, Aberg opened the scoring late in the first period, squeezing a shot from the right boards between goalie Roberto Luongo and the near post.
Nashville (3-1-0) regained the lead with 5:19 left in the second on Kevin Fiala's wrist shot that beat Luongo high to the glove side. The Predators selected the Swiss-born Fiala with the 11th pick in June.
Former Predators goalie Dan Ellis replaced Luongo at the start of the third period for Florida (0-1-2).
Aberg scored again at 6:22 of the third, and Austin Watson added an empty-net goal.
In the first game, Carter Hutton made 23 saves and stopped both Florida attempts in the shootout.
Smith scored for Nashville at 4:11 of the first period, converting a rebound of Garrett Noonan's shot. Smith led Nashville with 24 goals last season.
Brandon Pirri's power-play goal with 7:08 left in the third tied it at 1.
Al Montoya played the first two periods for Florida, before giving way to Sam Brittain in the third. Montoya stopped nine of 10 shots, and Brittain made 10 saves.
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