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.
Comment: 8 pages, 4 figures, accepted to PRC (letter)