Caroline Wozniacki and Mirjana Lucic-Baroni booked their spots in the Volvo Car Open quarter-finals as former champion Samantha Stosur bowed out.

Wozniacki, winner in Charleston in 2011 and runner-up two years prior, beat Australian qualifier Anastasia Rodionova 6-3 6-3 in the third round on Thursday.

The Danish fifth seed was relatively comfortable on her way to the last eight, having needed to come through a postponed second-round match earlier in the day.

Wozniacki overcame Annika Beck 7-5 6-1 before returning to get past Rodionova on the green clay at the WTA Premier event.

Awaiting her in the last eight is Jelena Ostapenko, who was on court for just 39 minutes and led Fanny Stollar 6-1 1-0 when the Hungarian retired.

Lucic-Baroni was challenged by fellow seed Kiki Bertens before the Croatian veteran completed a 7-6 (7-5) 6-4 win.

Up next for Lucic-Baroni is Shelby Rogers, who crushed Japanese teenager Naomi Osaka 6-4 6-2.

Meanwhile, Stosur's bid for a second Charleston title came to an end with a 7-5 6-3 loss to Irina-Camelia Begu.

The Romanian 10th seed managed to break serve four times in a largely comfortable win.

On a bad day for Australians, Daria Gavrilova also exited, losing 6-3 4-6 6-0 to Daria Kasatkina – Begu's quarter-final opponent.

The other last-eight clash is between Anastasija Sevastova and Laura Siegemund after their straight-sets wins.

Sevastova edged lucky loser Ons Jabeur 7-5 7-6 (8-6), while Siegemund continued her run with an upset 6-2 6-3 win over Lucie Safarova.

Germany's Siegemund has beaten seeds Venus Williams and Safarova to reach the quarter-finals.