  The $\mathrm{^{20}Ne(p, \gamma)^{21}Na}$ reaction is the slowest in the NeNa
cycle and directly affects the abundances of the Ne and Na isotopes in a
variety of astrophysical sites. Here we report the measurement of its direct
capture contribution, for the first time below $E\rm_{cm} = 352$~keV, and of
the contribution from the $E^{\rm }_{cm} = 368$~keV resonance, which dominates
the reaction rate at $T=0.03-1.00$~GK. The experiment was performed deep
underground at the Laboratory for Underground Nuclear Astrophysics, using a
high-intensity proton beam and a windowless neon gas target. Prompt $\gamma$
rays from the reaction were detected with two high-purity germanium detectors.
We obtain a resonance strength $\omega \gamma~=~(0.112 \pm 0.002_{\rm
stat}~\pm~0.005_{\rm sys})$~meV, with an uncertainty a factor of $3$ smaller
than previous values. Our revised reaction rate is 20\% lower than previously
adopted at $T < 0.1$~GK and agrees with previous estimates at temperatures $T
\geq 0.1$~GK.
  Initial astrophysical implications are presented.
