Belinda Bencic has beaten world number three Paula Badosa 2-6 7-6 (7-2) 6-4 to move on to the semi-finals of the Charleston Open.

Bencic, the 10th seed, appeared overmatched early on as she won less than half (12-25) of her service points in the opening set, getting her serve broken twice.

But as Bencic found her rhythm with her serve – winning 77 per cent of her first-serve points in the second set (24-31) – she wrestled the momentum away from Badosa, dominating the tie-break before breaking in the opening game of the third frame.

Bencic will face Ekaterina Alexandrova in the semi-final after the Russian dominated Magda Linette 6-0 6-2.

For the match, Alexandrova won 62 per cent of her points on serve (28-45) and 62 per cent of her points on return (26-42).

Fourth seed Ons Jabeur needed just 64 minutes to get the job done 6-3 6-2 against Anhelina Kalinina, winning 81 per cent of her successful first serves (29-36).

Jabeur will play 15th seed Amanda Anisimova in the semi-final after the American cruised past compatriot Coco Vandeweghe 6-1 6-2.

It was not a perfect performance from Anisimova, but she saved all five break points that she faced to never allow her opponent to get close.

Meanwhile, in Bogota at the Copa Colsanitas, top seed Camila Osorio is through to the semi-final after defeating Elina Avanesyan 6-1 6-4, where she will meet Laura Pigossi.

World number five and the tournament's top seed, Aryna Sabalenka, was upset by American Amanda Anisimova 3-6 6-4 6-3 in the third round at the Charleston Open.

Sabalenka's serve was the key to her early success, connecting on 73 per cent of her first serves, and winning 15 of the 19 points in that situation (79 per cent).

When Sabalenka's first serve percentage fell to 48 in the second set, Anisimova found her footing, breaking twice in the frame, before pouncing on the Belarusian's lacklustre second serve in the deciding set, winning seven of nine opportunities to earn the break and the win.

Sixth seed Jessica Pegula was also bounced in surprising fashion, losing 6-4 3-6 6-4 to unseeded compatriot Coco Vandeweghe.

In a razor-close contest, it came down to who took their chances, as Vandeweghe saved seven of the 10 break points she faced, while Pegula could only save one of five.

World number 10 Ons Jabeur had no problem navigating the challenge of Emma Navarro, winning 6-3 6-2 as she broke her opponent's serve on six occasions.

Canadian seventh seed Leylah Hernandez also fell victim to an unseeded upset, going down 3-6 6-3 6-4 against Poland's Magda Linette.

In a meeting between two top-10 seeds, Belinda Bencic got the better of Madison Keys to edge it 6-4 6-4.

Second seed Paula Badosa had to come from a set down to eventually get the better of Claire Liu 3-6 7-6 (10-8) 6-1.

In the late session, French 12th seed Alize Cornet went down in a close tussle against Ukraine's Anhelina Kalinina 7-6 (7-5) 7-5, while Jabeur won her second match of the day, beating Irina Begu 6-3 6-2.

Meanwhile, in Bogota at the Copa Colsanitas, top seed Camila Osorio dispatched Turkish opponent Ipek Oz 6-3 7-6 (7-4) to move on to the quarter-final where she will meet Elina Avanesyan.