On a day when multiple big names were dumped out of Wimbledon on the first day, Gauff stole the show on Court 1.
Despite being just 15 years old, and 24 years younger than Williams, Gauff showed few nerves as she combined power with great variety.
And on her fourth match point, the teenager sealed her place in the second round by completing a 6-4 6-4 victory.
The world No 313 burst into tears as a packed crowd on the newly-renovated Court 1 applauded her.
Before the tournament, Federer spoke glowingly about Gauff and praised Wimbledon chiefs for giving her a wildcard.
In her post-match press conference, Gauff was asked which players than inspired her along with Venus and Serena Williams.
And the young star revealed Federer took time to speak to her last year after defeat in the Australian Open juniors and reckons it helped her to then win French Open.
“Roger Federer definitely inspired me,” she said.
“When I lost first round Australian Open juniors, I talked to him. Gave me kind of a pep talk.
“The next tournament was French Open juniors, and I ended up winning it, so I guess it helped.
“Off-court heroes of mine, definitely Rihanna, Beyonce, I really look up to them as well.”
Gauff and Williams shared a moment at the net after the match and the youngster said her determination to win helped to maintain focus.
“On the court, I was not thinking about Venus. I was just playing my game,” Gauff said.
“No matter who I play against, I want to win. “So that’s what I was just thinking about the whole time.
“I wasn’t really thinking about who I was facing on the other side of the net.”
Gauff next plays Slovakia’s Magdalena Rybarikova on Wednesday.