Australians Samantha Stosur and Ajla Tomljanovic have won through to the third round of the Miami Open.

Stosur prevailed 6-4 6-4 over compatriot Ashleigh Barty in straight sets after the in-form wildcard came into the clash off a victory over former top-five player Eugenie Bouchard in Miami.

The match stayed on serve for much of the opening set until Stosur took advantage of a solitary break point.

The second was similarly tight. Barty had a number of chances to break but Stosur again seized a single advantage and held on.

Croatian-born Tomljanovic scored the upset of the tournament with her 3-6 6-4 7-5 victory over world No.13 and Indian Wells champion Elena Vesnina.

The 23-year-old world No.594, who is Nick Kyrgios’ girlfriend, led the Russian 5-3 in the third set on Thursday when a thunderstorm halted play.

She then returned on Friday (Saturday AEDT) and cashed in on her third match point.

The one-time world No.47 made her return last month after just over a year on the sidelines with a shoulder injury.

Vesnina, five days removed from the biggest victory of her career, committed a dozen double faults in the two hour, 12 minute match.

Venus Williams also overcame windy weather and an unfamiliar opponent in Brazilian Beatriz Haddad Maia to reach the third round later on Friday.

After rain delays pushed their match well into the night, the three-time champion moved past her 20-year-old challenger 6-4 6-3.

Williams told the Miami Herald she struggled with the conditions.

“It wasn’t easy out there, the wind felt like a gale force,” she said.

“I never saw her before. I didn’t know what to expect. I’m very impressed with her game and determination and that will take her very far.”

Top seed Angelique Kerber also prevailed in her evening match, beating Duan Yingying Duan 7-6(3) 6-2.

French Open champion Garbine Muguruza, whose opening match on Thursday was also interrupted, trailed 46th-ranked American Christina McHale 6-0 3-2 when play was suspended on Thursday but staved off a match point in the tiebreak before emerging with an 0-6 7-6(6) 6-4 victory.

Romanian third seed Simona Halep was pushed to three sets by Japanese teenager Naomi Osaka before advancing 6-4 2-6 6-3, while seeds Timea Babos and Roberta Vinci were eliminated.

American Madison Keys made quick work of Viktorija Golubic 6-1 6-2.