The Italian made it through another battle. This time, moving past Gianluca Mager, 6-1, 7-5, 3-6, 6-3, to face Mikael Ymer next.
Brady's affair with France's Fiona Ferro went down to the wire, but she scored a 6-4, 2-6, 7-5 win to set up a third-round clash with Gauff.
She rallied from 3-5 down in the second set and saved a set point to defeat Qiang Wang 6-3, 7-6(1). The teenager is through to a career best third-round showing in Paris.
The 22-year-old defeated Frenchman Gael Monfils, 6-0, 2-6, 6-4, 6-3, to become the first Swedish man to reach the third round in Paris since Robin Soderling in 2011.
The Pole rolled right past Rebecca Peterson, 6-1, 6-1, to set up a third-round match with Anett Kontaveit. Swiatek has only dropped seven games thus far.