Fifth seed Vondrousova, who stunned Jabeur to win Wimbledon last year, has form at Roland Garros, having lost out to Ashleigh Barty in the 2019 final.
She has had a mixed start to the year but did reach the semi-finals on the Stuttgart clay in the build-up to Roland Garros.
She recovered from going an early break down against Danilovic and saved four of the five break points she faced on her way to victory.
Gauff is also a former finalist at Roland Garros, having finished runner-up to the ever-dominant Swiatek in 2021.
Unlike many American players, Gauff has had plenty of experience of clay, having won the Roland Garros girls’ title as a junior in 2018.
She put all her experience to use against Cocciaretto, who had heavy strapping on her leg and looked to be feeling the effects of reaching the second week of a major for the first time.
Third seed Gauff moved well and played with some excellent control, breaking early in both sets and shaking off five double faults to close out victory in 60 minutes.
“I’m lucky – I’ve been able to train on clay since I was 10 years old, which is not common for Americans,” Gauff said.
“I like to slide and sometimes I do surprise myself.”