In a thrilling finish, Miller stumbled and then dived across the line as she edged out American world champion Allyson Felix to win in 49.44 seconds.
Felix took silver in 49.51 seconds with Jamaica's Shericka Jackson third.
"The only thing I was thinking was the gold medal and the next thing I know I was on the ground," Miller, 22, said. "It was just a reaction."
