High-precision mass measurements on neutron-rich zinc isotopes (71m,72-81)Zn have been performed with the Penning trap mass spectrometer ISOLTRAP. For the first time, the mass of 81Zn has been experimentally determined. This makes 80Zn the first of the few major waiting points along the path of the astrophysical rapid neutron-capture process where neutron-separation energy and neutron-capture Q-value are determined experimentally. The astrophysical conditions required for this waiting point and its associated abundance signatures to occur in r-process models can now be mapped precisely. The measurements also confirm the robustness of the N=50 shell closure for Z=30.