Gauff, nicknamed "Coco," is the youngest player in the Open era to advance through qualifying to reach Wimbledon's main draw, but she wasn't content to stop there and beat the 39-year-old Williams, one of her biggest idols, 6-4 6-4 in their first-round clash at the All England Club.
"I don't really know how to feel, this is the first time I've cried after a match, after winning," Gauff told the BBC.
The world No. 313 added: "I never thought this would happen. I'm living my dream right now, not many people get to say that."
Gauff revealed Williams said to her afterward: "Congratulations, keep going and good luck." She added: "I just told her I wouldn't be here if it wasn't for her, she's so inspiring. I've always wanted to tell her that but I've never had the guts to before.
"My parents will be super happy, my dad was jumping up every time I won a point. I'm so happy they spent all their time on me and my brothers and making sure we're successful."
'Raised for greatness'
Gauff won the first set in 35 minutes and held three match points in the second before Williams forced break point.
But the veteran could not convert her chance and Gauff made the most of her fourth match point to win in one hour 19 minutes on Wimbledon's No.1 Court.
Gauff was born in Georgia on March 13, 2004 to father Corey, a college basketball star, and mother Candi, a talented college track and field athlete. The family -- Cori has two younger brothers -- later moved to Delray Beach, Florida.
The teenager, who is coached by her father but has enjoyed spells training with Serena Williams' coach Patrick Mouratoglou in France, secured her spot at Wimbledon with a win in the final qualifying round at Roehampton, London Thursday.
She is the 12th youngest overall to play in the Wimbledon main draw, but the youngest to come through qualifying. She is also the youngest player to win a singles match at Wimbledon since Jennifer Capriati in 1991.
"Venus Williams, when the draw was coming out, would have been saying, 'please don't put me against Coco Gauff' because it's like looking in the mirror," three-time Wimbledon men's champion John McEnroe told BBC Sport.
"I don't say this lightly, but if she isn't No.1 by the time she is 20 I would be absolutely shocked."
Tracy Austin, a former women's world No.1, added: "People have been talking about her for years in the US and worldwide now people will recognize her.
"There were plenty of opportunities for her to get tight and the moment to overwhelm her but she was raised for greatness."
Last year, Gauff raised her profile by winning the French Open girl's championship. She also reached the quarter finals of junior Wimbledon.
This year, she became the youngest woman to win a grand slam qualifying match in the French Open.
In 2017, a then-13-year-old Gauff told CNN, "Overall, I want to be the best I can be and be the greatest," after becoming the youngest player to appear in a US Open junior final. Her current 301st WTA singles ranking has climbed sharply from 874 eight months ago.
By Rob Hodgetts,