Venus Williams held off a fightback from Heather Watson to win through to the quarter-finals of the Mubadala Silicon Valley Classic.

The number three seed is the highest ranked player left in the competition after both Garbine Muguruza and Madison Keys were forced to withdraw due to injury before their second-round matches.

Williams, 38, had raced into an early lead against Watson in San Jose, but the British player rallied in the second set to level the match.

Watson lost her momentum in the decider, however, and the American closed out the match in rapid fashion, winning 6-4 4-6 6-0.

She will next face Greece’s Maria Sakkari, who routed number eight seed Timea Babos 6-0 6-1.

Earlier, number five seed Mihaela Buzarnescu had defeated Amanda Anisimova 7-5 2-6 6-1, while Australia’s Ajla Tomljanovic beat Magdalena Frech 6-4 3-6 6-3.

At the Citi Open in Washington, Magda Linette stunned number three seed Naomi Osaka 6-2 3-6 6-3 to head into the final eight.

The Polish player had been a break down in the final set, but won four consecutive games – and the last 13 points in a row – to close out the upset in two hours and five minutes.

Linette, the world number 62, will take on number seven seed Donna Vekic in the quarter-finals after the Croatian prevailed in an epic deciding tie-break to win 6-2 3-6 7-6 (15/13) against Fanny Stollar.

Meanwhile, Svetlana Kuznetsova beat Ana Bogdan 6-2 6-1, eighth seed Yulia Putintseva defeated Jennifer Brady 7-5 6-2 and Saisai Zheng overcame Ysaline Bonaventure 6-4 6-4.