The US team recorded a season's best of 3 minutes 19.06 seconds to defeat Jamaica by 1.28 seconds on Saturday. Britain claimed bronze in 3:25.88, Xinhua news agency reported.
Courtney Okolo gave the US an early lead and it was maintained for the rest of the race by Natasha Hastings, Phyllis Francis and Allyson Felix.
It was Felix's third medal of these Games following her gold in the 4x100m relay and silver in the 400m.
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