Struggling with a flu since arriving in Taipei, Svitolina, ranked 13th, narrowly defeated the 181th-ranked Jabeur 6-1, 3-6, 7-6 (7/4) to set up a meeting with Luxembourg's Mandy Minella on Saturday.
China's Shuai Peng saw off second-seed Samantha Stosur of Australia 6-4, 6-4 to make her way into the semi-finals against Czech Lucie Safarova.
Peng, ranked 71st, returned to tennis last March after taking a break from playing following an operation for a waist injury in 2015.
Safarova beat sixth-seed Misaki Doi of Japan 6-4, 7-6 (7/1) while Minella overcame China's Lin Zhu 1-6, 6-3, 7-5 to advance to the last four.