Centrowitz produced the biggest upset on the final night of track competition, beating defending champion Taoufik Makhloufi of Algeria into second place to win 1500m gold in 3min 50.00sec.
Centrowitz became the first American man in more than a century to win the event, which has been shared exclusively between African runners since 1996.
The last American to win the Olympics 1500m was Mel Sheppard in the 1908 London Games.
“There’s nothing like it. It doesn’t compare to anything else I’ve won in my life,” said Centrowitz. “Doing my victory lap, I literally kept screaming to everyone I know ‘Are you kidding me?”