The American was seeking to make the semi-finals at a Grand Slam for the third time this season, having last achieved the feat back in 2002.

Williams made a fine start to the match, as the 37-year-old claimed the opening set 6-3 against her Czech opponent on Arthur Ashe Stadium.

Kvitová, who returned to action in May after an attacker at her home in December stabbed her in the hand, hit back to win the second 6-3 to force a decider.

Neither player was able to make a telling breakthrough in the final set, leaving the contest to be decided on a tie-break.

Williams would win the tie-break 7-2 to seal a 6-3, 3-6, 7-6 victory and advance to the last four of the competition.

She will now face fellow American Sloane Stephens in the semi-finals as she seeks to better her runner-up finishes at the Australian Open and Wimbledon this year.

Stephens also progress via a third set tie-break, as the 24-year-old overcame Latvia's Anastasija Sevastova 6-3, 3-6, 7-6.

As the prospect of home success in the women’s event rose, the American challenge in the men’s competition drew to a close.

South Africa's Kevin Anderson progressed to his first Grand Slam semi-final, as he defeated home favourite Sam Querrey.

Anderson emerged as a 7-6, 6-7, 6-3, 7-6 to reach the last four.

He will face the challenge of Pablo Carreno Busta, as the Spaniard ended Diego Schwartzman’s run.

Busta, the tournament 12th seed, beat his Argentine opponent 6-4, 6-4, 6-2.