Bulk ZrO2 is both nonreducible and nonmagnetic. Recent experimental results show that dopant-free, oxygen-deficient ZrO2-x nanostructures exhibit a ferromagnetic behavior at room temperature (RT). Here, we provide a comprehensive theoretical foundation for the observed RT ferromagnetism of zirconia nanostructures. ZrO2 nanoparticles containing up to 700 atoms (3 nm) have been studied with the help of density functional theory. Oxygen vacancies in ZrO2 nanoparticles form more easily than in bulk zirconia and result in electrons trapped in 4d levels of low-coordinated Zr ions. Provided the number of these sites exceeds that of excess electrons, the resulting ground state is high spin and the ordering is ferromagnetic. The work provides a general basis to explain magnetism in intrinsically nonmagnetic oxides without the help of dopants.