By SABC Sport
31st May 2024
The US Open champion, a finalist in Paris in 2022, won 6-2 6-4 to set up a meeting with Italian Elisabetta Cocciaretto.
Gauff, 20, squandered a match point at 5-2 in the second set and faced three break points at 5-4.
But she got over the line eventually when Ukrainian Yastremska, the 30th seed, wafted a forehand wide.
"It's one match at a time," said Gauff. "It's important to stay in the moment. It's important to expect great things from yourself but I'm 20 â- and I'm hoping to be playing for another 10 years or so."
Cocciaretto, had earlier knocked out 17th seed Liudmila Samsonova of Russia 7-6 (4) 6-2.
"I played her in Dubai this year and she's definitely a fighter," added Gauff.
"It's not an easy match, she's one of those players who doesn't give up until you shake hands. It'll be a difficult match but I'm ready."