Sabalenka had taken the first set 6-1 before Romanian Ruse retired with a thigh problem in the first game of the second.

Japan’s Osaka survived a scare to eventually overcome American wild card Hailey Baptiste in a match lasting nearly three hours.

World number 98 Baptiste was a break up and serving at 4-3 in the decisive third set, but Osaka came back well.

The four-time Grand Slam champion held serve before breaking Baptiste again to take the match 7-6 (8-6) 3-6 6-4 in two hours, 59 minutes and 57 seconds – the longest women’s match of the tournament so far.

There were no such problems for third seed Gauff, who continued her fine tournament with a comfortable straight-set win over Greece’s Maria Sakkari.

The 21-year-old world number three, who needed just 47 minutes to beat Sofia Kenin 6-0 6-0 in the previous round, won 6-2 6-4 to reach the last 16 in Miami for the third time in her career.

Italian sixth seed Jasmine Paolini also went through after Tunisian opponent Ons Jabeur retired injured when trailing 4-3 in the first set.