We demonstrate enhancement of the photoluminescence (PL) properties of individual zero-dimensional (0D) Cs4PbBr6 perovskite nanocrystals (PNCs) upon encapsulation by alumina using an appropriately modified atomic layer deposition method. In addition to the increased PL intensity and improved long-term stability of encapsulated PNCs, our single-particle studies reveal substantial changes in the PL blinking statistics and the persistent appearance of the long-lived, “delayed” PL components. The blinking patterns exhibit a modification from the fast switching between fluorescent ON and OFF states found in bare PNCs to a behavior with longer ON states and more isolated OFF states in alumina-encapsulated PNCs. Controlled exposure of 0D nanocrystals to moisture suggests that the observed PL lifetime changes may be related to water-induced “reservoir” states that allow for longer-lived charge storage with subsequent back-feeding into the emissive states. Viable encapsulation of PNCs with metal oxides that can preserve and even enhance their PL properties can be utilized in the fabrication of extended structures on their basis for optoelectronic and photonic applications.