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The 17O(p,α)14N 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 17O and 18F, which can provide constraints on astrophysical models. A new direct determination of the ER=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±1.4stat±0.7syst neV, thanks to a significant background reduction underground and generally improved experimental conditions. The (bare) proton partial width of the corresponding state at Ex=5672 keV in 18F is Γp=35±5stat±3syst neV. This width is about a factor of 2 higher than previously estimated, thus leading to a factor of 2 increase in the 17O(p, α)14N reaction rate at astrophysical temperatures relevant to shell hydrogen burning in red giant and asymptotic giant branch stars. The new rate implies lower 17O/16O ratios, with important implications on the interpretation of astrophysical observables from these stars.