The American is the youngest woman to qualify for the tournament in the Open era but she played like a veteran in an excellent 6-4 6-4 victory.
Gauff served superbly, being broken only once, and showed tremendous composure in her first main draw match at a grand slam, making just eight unforced errors compared to 25 for her 39-year-old opponent.
Gauff said her phone had been "banging" since her win.
She said: "My grandma called me. My brother, he called me.
"He said his chest is out, he's going to brag to all his friends. He texted me, 'Happy 40K followers' because I gained some followers after the match.
"All my friends are texting me. I'm going to be up all night trying to respond to everybody."
The American schoolgirl, who recently sat a science test, was asked how she would grade her performance at Wimbledon.
She said: "On my science test, I got a B. Today I'd give myself an A. Hopefully my next test I can get an A, but you never know."
Williams won two of her five Wimbledon singles titles before Gauff was born and this was only the second time she has been beaten in the first round since her debut in 1997.
While Williams has been setting records at one end of the age scale, Gauff has been breaking them at the other, reaching her first junior slam final at the US Open aged just 13.
She won the French Open title last year and, on this evidence, she is more than ready to make a big impression in the senior game.
Gauff was inspired to pick up a racket by the Williams sisters and for Venus it must have been like facing a teenage version of herself as her opponent fired down serves over 110mph and scampered around the court with her long levers.
A tense game saw Williams save three match points before creating one break point, which Gauff saved with a 108mph second serve.
When her fourth opportunity came, the teenager took it, then dropped to the court in disbelief.
The teenager revealed she listened to music when stepping onto court to help keep her calm.
"Before the match I was listening to 'Icon' by Jaden, 'Humble' by Kendrick Lamar," she said.
"When I walked on the court, I was listening to 'Rice Street' by Miss Mulatto. She's a new upcoming female rapper."
After getting emotional following her win on No. 1 Court, Gauff was asked when she last cried.
She said: "Well, this was the last time I cried. But before then, oh, actually the movie 'End Game' when Ironman died, I was crying.
"Every time I think of it, I get teary-eyed because I really liked Ironman."