Fluorine is one of the most interesting elements in nuclear astrophysics, where the ^{19}F(p,α)^{16}O reaction is of crucial importance for Galactic ^{19}F abundances and CNO cycle loss in first generation Population III stars. As a day-one campaign at the Jinping Underground Nuclear Astrophysics experimental facility, we report direct measurements of the essential ^{19}F(p,αγ)^{16}O reaction channel. The γ-ray yields were measured over E_{c.m.}=72.4-344 keV, covering the Gamow window; our energy of 72.4 keV is unprecedentedly low, reported here for the first time. The experiment was performed under the extremely low cosmic-ray-induced background environment of the China JinPing Underground Laboratory, one of the deepest underground laboratories in the world. The present low-energy S factors deviate significantly from previous theoretical predictions, and the uncertainties are significantly reduced. The thermonuclear ^{19}F(p,αγ)^{16}O reaction rate has been determined directly at the relevant astrophysical energies.