Modeling the composition of neutron-star crusts depends strongly on binding energies of neutron-rich nuclides near the N = 50 and N = 82 shell closures. Using a recent development of time-of-flight mass spectrometry for on-line purification of radioactive ion beams to access more exotic species, we have determined for the first time the mass of (82)Zn with the ISOLTRAP setup at the ISOLDE-CERN facility. With a robust neutron-star model based on nuclear energy-density-functional theory, we solve the general relativistic Tolman-Oppenheimer-Volkoff equations and calculate the neutron-star crust composition based on the new experimental mass. The composition profile is not only altered but now constrained by experimental data deeper into the crust than before.