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Couch, 27, scored highly in her third dive after a poor start to finish in 10th place with 318.00 points.
Chinese 17-year-old Si Yajiei scored consistently well to finish in first place with 389.30 points.
Synchronised 10m silver medallist Pandelela Rinong of Malaysia also reached the final, which begins on Thursday at 20:00 BST.
Great Britain's Tonia Couch has qualified for the women's Olympic diving 10m platform final.