The U.S. finished in 3 minutes 19.06 seconds. Jamaica took silver in 3:20.34 and Britain the bronze in 3:25.88.
"It's really special," said four-time Olympian Felix who had started the Games somewhat frustrated after missing out on qualification for the 200m.
"I can look back on the things that I've accomplished and really be proud and really grateful for what track and field has brought to my life"
Her team mate Courtney Okolo set the stage for the win by grabbing the lead in the opening stage and the U.S. never relinquished it, pushed by Jamaica but well clear of the rest of the field by the halfway point.
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Felix held off a late challenge by Jamaica's Novlene Wiliams-Mills to claim her third medal of the Rio Olympics having won gold in the 4x100m relay and silver in the individual 400m.
The U.S. gold streak in the event started at the 1996 Atlanta Games.
"It's amazing to come together with these women tonight and be able to finish it off," Felix said. "It was a good night."
Natasha Hastings and Phyllis Francis rounded out the U.S. team.
Jamaica's silver was their fifth straight medal in the event, following silver in 2000 and bronze in 2004, 2008 and 2012 while Britain claimed their first medal since 1992.
(Reporting by Scott Malone, editing by Mitch Phillips)
