Switzerland's Bencic, seeded fourth, won her ninth straight match in Charleston when she beat seventh-seeded Ekaterina Alexandrova 6-3, 6-3.

Second-seeded Ons Jabeur advanced when Anna Kalinskaya retired from their quarter-final because of illness.

Jabeur was up 6-0, 4-1 when Kalinskaya called it a day, the Tunisian reaching the semi-finals for the third straight year.

She will next face third-seeded Daria Kasatkina, who turned the tables on ninth-seeded American Madison Keys 6-7(5), 6-4, 6-2 in a battle of former Charleston champions.

Kasatkina notched just her second victory over Keys in 10 career meetings.

Pegula, ranked third in the world, needed just 35 minutes to capture the opening set from Badosa, and broke to open the second.

Powering through her service games, Pegula served for the match at 5-4 only for Badosa to break and level the set.

The Spaniard held off a break point in the next game as they went to the tiebreaker, where she saved a match point with a forehand winner before giving Pegula another with a forehand long, her backhand into the net finally allowing Pegula to celebrate.

Pegula, who is seeking her first clay court title, will have her work cut out against Bencic, who is chasing her third title of the season after victories in Adelaide and Abu Dhabi.

Jabeur, who improved to 2-0 against Kalinskaya and reached her second semifinal of the season.

The first was in Adelaide in January. Since then Jabeur - the beaten finalist at Wimbledon and the US Open last year - has undergone surgery after suffering a knee injury at the Australian Open.

She missed the WTA's tournaments in Doha and Dubai, and after falling in the third round at Indian Wells lost her second-round opener at Miami.

However, Jabeur has looked at home on the green clay at Charleston, reaching the semis without dropping a set.