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.
"It's a relief," Rollins told reporters.
"There has been such a lot of anticipation. I have younger brothers and as the oldest I like to lead by example - even from far away."
Ali came a clear second while Castlin had to hold off a late challenge from Britain's American-born Cindy Ofili to claim bronze.
"I would like to dedicate this medal to victims of gun violence," Castlin said.
"Women hurdlers are so strong in the US and we have overcome controversy. We are three strong hurdlers."
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.
Reigning world champion Bartoletta left it late to take high jump gold -- securing victory with her fifth jump to knock compatriot Reese down into the silver medal position.
Bartoletta jumped a season's best of 7.17m with just one jump remaining. Serbia's Ivana Spanovic came third.
"I couldn't really celebrate," Bartoletta, who won her first world title back in 2005, told reporters.
"I kept thinking that at any moment that someone can jump something huge.
"Then, when I won, I realized that I have to be back in the morning for the relay."
Darya Klishina, the only Russian athlete to feature in the track and field events at Rio 2016, failed to qualify for the final three rounds of jumping after posting a disappointing 6.63m.
While the US enjoyed a stellar night on the track there was also success for Jamaica's Elaine Thompson who added the 200-meters title to her 100-meters gold.
The Jamaican ran a season's best of 21.78secs to overcome Dutch favorite Dafne Schippers who came second with America's Torie Bowie taking bronze.
Thompson's success makes her the first women to win Olympic gold in the 100m and 200m events since Florence Griffith Joyner did so in 1988.
"My school motto was 'let the light shine' and I let my light shine tonight," Thompson told reporters.
"It's a big surprise to me because I have had a hamstring injury.
"You must overcome these things and tonight I am standing here with a gold. To beat Dafne is a hard run."