Recent in vitro investigations of N,N′-bis(salicylidene)-1,2-phenylenediamine (SAP) iron(III) complexes substituted with alkyl (ethyl, propyl, butyl) carboxylates at position 4 in tumor and leukemia cells revealed strong cytotoxic activity. In continuation of this study, analogous nickel(II) and cobalt(III) complexes were synthesized and tested in HL-60 leukemia, and cisplatin-sensitive and -resistant A2780 ovarian cancer cell lines. The biological activity depended on the extent of cellular uptake and the formation of reactive oxygen species (ROS). Inactive [(Ni(II) SAP] complexes (1−3) only marginally accumulated in tumor cells and did not induce ROS. The cellular uptake of [Co(III)SAP]Cl complexes (4−6) into the cells depended on the length of the ester alkyl chain (ethyl, 4 < propyl, 5 < butyl, 6). The cytotoxicity correlated with the presence of ROS. The low cytotoxic complex 4 induced only few ROS, while 5 and 6 caused a good to outstanding antiproliferative activity, exerted high ROS generation, and induced cell death after 48 h. Necrostatin-1 prevented the biological effects, proving necroptosis as part of the mode of action. Interestingly, the effects of 5 and 6 were not reversed by Ferrostatin-1, but even enhanced upon simultaneous application to the tumor cells.