Badosa reached the last four by defeating China’s Zhang Shuai in straight sets.
The Spaniard saw off the wildcard 6-1 7-6 (7-4) in one hour 23 minutes, although she had to fight back from 1-3 down in the second set.
Badosa was ranked 140 in the world earlier this year, but has risen to 19th after 28 wins in 35 matches since May.
The remaining quarter-finals will take place on Friday with top seed Aryna Sabalenka facing Karolina Muchova, and Mirra Andreeva taking on fifth seed Qinwen Zheng.
Meanwhile, Britain’s Billy Harris exited the Shanghai Masters in the opening round, losing 6-3 6-4 to Italy’s Mattia Bellucci.
