Ahead of the match, Cori told BBC Sport how the Williams sisters were her idols and Serena was "the reason why I play tennis".
Cori "Coco" Gauff reacting after she won the first set against Venus Williams on Monday.
Gauff will face a tough test in the second round, where she meets Magdalena Rybarikova of Slovakia, who pulled off a shock of her own by seeing off 10th seed Aryna Sabalenka in straight sets in their first-round match. Osaka famously beat Serena Williams to win the U.S. Open past year.
Both players are among the younger generation expected to eventually replace the Big Three of Roger Federer, Rafael Nadal and Novak Djokovic in men's tennis.
Gauff produced a flawless performance in one hour and 19 minutes, and she told the BBC: "I don't really know how to deal with it - that's the first time I cried after a match, winning. But I just don't know how to explain how I feel".
"The Williams family in general made me realize that it was possible", he told the New York Times.
"I told Venus after the match "thank you" - I wouldn't be here if it wasn't for her".
Zverev lost to Jiri Vesely of the Czech Republic 4-6, 6-3, 6-2, 7-5, while Tsitsipas was beaten by Thomas Fabbiano of Italy 6-4, 3-6, 6-4, 6-7 (8), 6-3.
"She used her powerful serve and all-court game to overwhelm her 39-year-old opponent", the Guardian reported. "And I was just telling her that she's so inspiring". Her tennis career began at age eight.
In 2017, Gauff reached the U.S. Open girls' final at just 13 before going on to win the French Open girls' singles title a year later.
She showed plenty of grit in this match, particularly after getting broken to make it 4-all in the second set.
A few days after turning 20, the left-hander struggled to get to grips with her opponent's game as she lost in the first round for the third successive year.
French Open finalist Marketa Vondrousova was knocked out in the first round at Wimbledon, losing 6-4, 6-4 to Madison Brengle of the United States.
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