The 24-year-old is only the second athlete from the US territory to win an Olympic gold medal, after Monica Puig in the women’s tennis singles in 2016.
An emotional Camacho-Quinn said it “meant a lot” after she stormed across the line in 12.37 seconds.
“I wanted to be a gold medallist and I got it,” she said.
World indoor champion Kendra Harrison took silver, to give the US a medal in the women’s sprint hurdles for the sixth Olympic Games in a row – the longest medal streak by a single nation in this event in the history of the Games.
Jamaica’s Megan Tapper won bronze.
Greek long jumper Miltiadis Tentoglou provided another first – his country’s first gold in the event – but had a less serene route to the top of the podium, the 23-year-old struggling in the early rounds and outside the medal positions before his final attempt.
However, the 2021 world leader said he “managed to pull something out” in his last jump, sealing the Olympic title with a leap of 8.41m to tie the mark of Juan Miguel Echevarria and pip the Cuban to gold by virtue of a longer second-best jump.
“I want to thank all my supporters back home in Greece,” he said. “They are awake right now, supporting me. It’s six in the morning maybe. So thanks to them.”
Cuba’s Maykel Masso took bronze.
Elsewhere in Monday’s action, Jamaica’s 100m bronze medallist Shericka Jackson failed to progress to the women’s 200m semi-final, finishing fourth in her heat.
The 27-year-old looked as though she eased up metres before the line, missing one of the qualification places by four one-thousandths of a second.
In another dramatic moment, the Netherlands’ Sifan Hassan fell at the bell in her 1500m heat.
However, the world champion at the distance quickly got back to her feet and went on to cross the line first in 4:05.17.
She is seeking a treble of 1500m, 5,000m and 10,000m success – a target that sees her potentially having to run six gruelling races in eight days.