The United States had trailed almost the entire game when they began the final quarter 53-49 down, but they dug deep and exploded with a 14-5 run at the start of the fourth that turned the game around.
Rutgers guard Matee Ajavon poured in 27 points - shooting 11 of 18 (61%) form the field - with Louisville forward Angel McCoughtry collecting 17 points and nine rebounds.
Natasha Humphrey added 11 points with three of five shooting from three-point range while Tennessee's Nicky Anosike 10 points.
The United States made 33 of 65 shots (51%) from the field.
"This feels terrific. We came down here as the youngest team in the tournament, but they also came out here with the biggest hearts," said coach Dawn Staley. "I thought we had a shot of winning it because they all bought into the USA Basketball system which is a no star system. Everybody played their roles to the fullest and that's why we won. If it was any other way I think we could of come up short today."
"It was a very difficult, exciting game right to the end," said Ajavon. "I think Brazil, despite being more experienced, could not handle the pressure of playing at home. We focused on our goal and it brought us victory.
"This gold medal is the result of hard work and training. It's an honor to be a Pan American champion."
Brazil, which was giving an emotional farewell to coach Antonio Carlos Barbosa and captain Janeth Arcain, had taken a 8-6 lead early in the game and finished the first quarter with a 19-18 advantage. They extended that to 30-25 early in the second but could not shake off their opponents and the gap was back to one 34-33 at half-time.
The energy then seemed to fade from Brazil as the United States took control.
Micaela Jacinto scored 21 points and Adriana Pinto 19, while Arcain signed off with 14 and seven rebounds.
"Today was like having a movie in my head from the beginning of my career right to saying goodbye," said Arcain. "Without a doubt, giving up playing has been much more difficult than starting out."
"The United States did everything to win," added Jacinto. "They attacked, defended well and didn't allow us to advance. We tried but we couldn't stop them. We will Janeth a lot."
Cuba had earlier claimed bronze by beating Canada 62-49.
The game was straightforward enough for the Cubans, who had come to Brazil has defending champions.
They led 18-12 at the end of the first quarter and extended that to 30-23 by half-time before pulling further away as the game went along.
Yakelin Plutin scored 20 points while Suchitel Avila added 12 and captain Yalma Boulet 11 for Cuba.
"Our aim was to win gold, but we didn't make it, so I'm very happy with bronze," said Boulet. "This medal has great value for our team. The crowd really helped us do a good job. That was amazing."
Sarah Crooks was the only Canadian to score in double figures as her team struggled offensively thoughout, shooting just 18 of 60 (30%). Particularly poor was their long range shooting as they made only 1 of 14 (7%) from beyond the arc.
"We played to win a medal and fourth place is not so good," said Canada coach Allison McNeill. "The girls were tired and they are very inexperienced. We haven't had any rest days. We responded well to situations several times during the game, but it wasn't enough to win.
"Tereza Gabriele was injured so we struggled with our three pointers."
Colombia edged out Argentina 59-58 to take fifth place in a game that went to the wire.
Colombia had raced out to an 11-5 lead in the early minutes of the game but trailed 33-31 at half-time.
That had becone a 50-41 advantage at the end of the third period but Colombia began the final period on an 8-2 run to get back into the game, only to come up just short.
Levys Torres was the star of the show for Colombia with 16 points and 12 rebounds while Yaneth Arias added 15 points and Elenda Diaz 13.
Marcela Paolette led Argentina with 16 points while Laura Nicolini had 15 points and 10 rebounds.
Brisa Silva scored 19 points to lead Mexico to seventh place with a 63-56 win over Jamaica.
Abril Garcia added 15 points and Erika Gomez 11.
Nicole Louden led Jamaica with 13.