The 19F(p, α)16O reaction is an important fluorine destruction channel in the proton-rich outer layers of asymptotic giant branch (AGB) stars and it might also play a role in hydrogen-deficient post-AGB star nucleosynthesis. So far, available direct measurements do not reach the energy region of astrophysical interest (E cm 300 keV), because of the hindrance effect of the Coulomb barrier. The Trojan Horse (TH) method was thus used to access this energy region, by extracting the quasi-free contribution to the 2H(19F, α16O)n and the 19F(3He, α16O)d reactions. The TH measurement of the α0 channel shows the presence of resonant structures not observed before, which cause an increase of the reaction rate at astrophysical temperatures up to a factor of 1.7, with potential consequences for stellar nucleosynthesis.