After Suarez overcame a 5-1 deficit to tie the second set at 5, Stephens broke serve for a 6-5 lead and scored four straight points to put away the match, ending it with a sharp cross-court forehand.
“Maybe the old me would have kind of freaked out,” Stephens said. “I was kind of like, `OK, it’s fine, she’s allowed to play well. Just kind of regroup.’ I did that. I was happy with that.”
The 25-year-old Stephens, ranked No. 3 in the world, won a hard-court title in Miami in March and lost the French Open final to top-ranked Simona Halep. In the quarterfinals, the American will face Anastaija Sevastova of Latvia, a 6-3, 7-6 (2) winner over 10th-seeded Julian Goerges of Germany. Sevastova, ranked 19th, won last month in Bucharest.
Ashleigh Barty, the 15th seed from Australia, beat France’s Alize Cornet 7-6 (3), 6-4. Barty will face Kiki Bertens of the Netherlands, a 6-3, 6-2 winner over eighth-seeded Petra Kvitova of the Czech Republic.
In rain-delayed, second-round matches, Halep topped Russia’s Anastasia Pavlyuchenkova 7-6 (9), 4-6, 7-5; the 20-year-old Sabalenka upset second-seeded Caroline Wozniacki of Denmark 5-7, 6-2, 7-6 (4); Konta beat Victoria Azarenka of Belarus 6-3, 6-1, and Williams edged Romania’s Sorana Cirstea 7-6 (4), 6-4.