Deportivo equalized through Ruben Castro with six minutes to go but Dady got the Osasuna's winner two minutes before the whistle with a left foot free kick from 20m out.
Valencia's woes increased just four days after they failed to qualify for the knockout stages of the Champions League when they crashed 3-0 at home to Athletic Bilbao.
It was the Basques first win in Valencia's Mestalla stadium for 20 years.
RSS