The USA took the lead in the first period and never trailed in the game - but their opponents were no more than two goals behind at any stage.
Hungary have never claimed a Water Polo medal at an Olympic Games since the first competition at Sydney 2000.
The USA are in the hunt for their first gold medal, after winning a silver four years ago, and finishing on the podium in both previous Games.
Maggie Steffens scored seven for the winning side, while Courtney Mathewson found the back of the net four times.
Captain Brenda Villa, Kelly Rulon and Kami Craig each scored one goal.
Barbara Bujka scored four for Hungary, Dora Antal netted three, and Gabriella Szucs scored two.
Orsolya Takacs, captain Rita Dravucz, Ildiko Toth and Dora Csabai scored one goal.