Biles won her 21st World Championships gold medal in Friday's all-around event, with Andrade, the reigning champion, finishing second.
But the order was reversed on Saturday as a near flawless Andrade won by a margin of 0.201 points.
Algeria's Kaylia Nemour took the silver while American Shilese Jones took the bronze medal.
Qiu scored a total of 15.100 points to claim the gold medal.
Ahmad Abu Al Soud of Jordan took the bronze medal but missed out on automatic Olympic qualification.
Persons:
Brazil's Rebeca Andrade, Yves Herman Acquire, Rebeca Andrade, Simone Biles, Biles, Andrade, Simone, Qiu, Kaylia Nemour, Shilese Jones, MCCLENAGHAN, Ireland's Rhys McClenaghan, Young, Ahmad Abu Al Soud, Jordan, Max Whitlock, Israel's Artem Dolgopyat, Kazuki Minami, Milad Karimi, Yang Liu of, Eleftherios Petrounias, Hao, Trevor Stynes, Toby Davis
Organizations:
Rights, American, Kazakhstan, Thomson
Locations:
Antwerp, Belgium, Rights ANTWERP, Friday's, China, American, British, Yang Liu of China, Greece