  The $^{17}$O(p,$\alpha$)$^{14}$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 $E_{\rm R}~=~64.5$~keV resonance strength performed at the Laboratory for
Underground Nuclear Astrophysics accelerator has led to the most accurate value
to date, $\omega\gamma = 10.0 \pm 1.4_{\rm stat} \pm 0.7_{\rm syst}$~neV,
thanks to a significant background reduction underground and generally improved
experimental conditions. The (bare) proton partial width of the corresponding
state at $E_{\rm x} = 5672$~keV in $^{18}$F is $\Gamma_{\rm p} = 35 \pm 5_{\rm
stat} \pm 3_{\rm syst}$~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,$\alpha$)$^{14}$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.
