Rollins, who finished ahead of teammates Nia Ali and Kristi Castlin in a thrilling final, cruised home in a time of 12.48 seconds.
It was the second gold medal of the night for the US after Tianna Bartoletta triumphed in the long-jump with fellow American Brittney Reese coming second.
Rollins, the 2013 world champion, had looked good in qualifying for the final and showed her class in beating her teammates.
Ali came a clear second while Castlin had to hold off a late challenge from Britain’s American-born Cindy Ofili to claim bronze.
The triumph was a sign of the US’s recent domination of the event.
Seven different American women have clocked the fastest seven times in the world this year — including world record holder Kendra Harrison, who didn’t even make the US team for Rio.