World number one and French Open champion Swiatek eased past Italy's Jasmine Paolini 6-3, 6-0 in just 67 minutes. Victory was a relief for the 21-year-old Pole who had suffered early losses at warm-up events in Toronto and Cincinatti. "In matches, being a little bit stressed and tight, it can get a little bit worse, but still, I feel like my level is just better," said Swiatek who next faces 2017 champion Sloane Stephens. "We'll see if I'm going to hold on to that." Alcaraz, the 19-year-old world number four, was made to sweat by battling Sebastian Baez, winning the first two sets 7-5, 7-5 before the Argentine retired injured 0-2 down in the third.