Third-order pair energies and the total third-order energy are obtained for the first time for an atomic system containing 3d electrons. The variational-perturbation method is applied within the framework of the Rayleigh-Schrödinger perturbation theory with H0=HHF. The N-electron first-order wave function is defined in terms of orbital configurations of one-electron functions and symmetry-adapted pair functions in the form of partial-wave (PW) expansions. Extensive basis sets including all PW up to l,l'≤9 are used. For Zn2+ the total third-order energy amounts to about 9% of the second-order energy obtained in the same basis set, which is considerably more than for closed-shell ten-electron systems. Values of the energy functional for the function ψ0+λψ1 are also reported. The latter represent the most accurate variational results obtained so far for atomic systems containing 3d electrons.