The ^{19}Ne(p,γ)^{20}Na reaction is the second step of a reaction chain which breaks out from the hot CNO cycle, following the ^{15}O(α,γ)^{19}Ne reaction at the onset of x-ray burst events. We investigate the spectrum of the lowest proton-unbound states in ^{20}Na in an effort to resolve contradictions in spin-parity assignments and extract reliable information about the thermal reaction rate. The proton-transfer reaction ^{19}Ne(d,n)^{20}Na is measured with a beam of the radioactive isotope ^{19}Ne at an energy around the Coulomb barrier and in inverse kinematics. We observe three proton resonances with the ^{19}Ne ground state, at 0.44, 0.66, and 0.82 MeV c.m. energies, which are assigned 3^{+}, 1^{+}, and (0^{+}), respectively. In addition, we identify two resonances with the first excited state in ^{19}Ne, one at 0.20 MeV and one, tentatively, at 0.54 MeV. These observations allow us for the first time to experimentally quantify the astrophysical reaction rate on an excited nuclear state. Our experiment shows an efficient path for thermal proton capture in ^{19}Ne(p,γ)^{20}Na, which proceeds through ground state and excited-state capture in almost equal parts and eliminates the possibility for this reaction to create a bottleneck in the breakout from the hot CNO cycle.