The ^{17}O(p,α)^{14}N reaction plays a key role in various astrophysical scenarios, from asymptotic giant branch stars to classical novae. It affects the synthesis of rare isotopes such as ^{17}O and ^{18}F, which can provide constraints on astrophysical models. A new direct determination of the E_{R}=64.5 keV resonance strength performed at the Laboratory for Underground Nuclear Astrophysics (LUNA) accelerator has led to the most accurate value to date ωγ=10.0±1.4_{stat}±0.7_{syst} neV, thanks to a significant background reduction underground and generally improved experimental conditions. The (bare) proton partial width of the corresponding state at E_{x}=5672 keV in ^{18}F is Γ_{p}=35±5_{stat}±3_{syst} neV. This width is about a factor of 2 higher than previously estimated, thus leading to a factor of 2 increase in the ^{17}O(p, α)^{14}N reaction rate at astrophysical temperatures relevant to shell hydrogen burning in red giant and asymptotic giant branch stars. The new rate implies lower ^{17}O/^{16}O ratios, with important implications on the interpretation of astrophysical observables from these stars.