The Romanian was blown away in an opening-set tie-break, but hit back to win the second 6-1.
After finding herself 3-0 down in the decider, Bogdan then showed her fighting spirit once more to triumph 6-7 (3-7) 6-1 6-4 after two and a half hours on court.
It capped an impressive upset for the 21-year-old, who is ranked 241 in the world, 144 places below her Chinese opponent.
"It was such a tough match, against a top 100 player, but I am really happy that I won, I really kept fighting to the end," Bogdan told reporters.
"It was not easy to play against her, I knew I had to be really aggressive but everything came good for me in the last set when I came back from 3-0."
Bogdan will face sixth seed Vitalia Diatchenko in the final four, after the Russian breezed past Thai second seed Luksika Kumkhum 6-2 6-3.
Top seed Anna-Lena Friedsam is also in the hat after beating Poland's Magda Linette.
Lena-Friedsam was made to work for her triumph once again as, after two three-set matches in as many days, she had to come through a first set tie-break before eventually prevailing 7-6 (7-0) 6-4.
Standing between Friedsam and the final will be home wildcard Chan Yung-Jan, after the 25-year-old upset fourth seed Alla Kudryavtseva 6-3 3-6 6-1.