Platinum(IV) complexes offer the potential to overcome cisplatin resistance of cancer cells, with possible improved selectivity. Resveratrol, a natural polyphenol with anticancer and antioxidant capacity, could limit the possible side effects of chemotherapeutics on healthy cells. This study investigates the effects of platinum(IV) complexes containing some esters of the ethylenediamine-N,N′-di-S,S-(2,2′-dibenzyl)acetate acid (H2-S,S-eddba), and resveratrol on proliferation, migration, and redox balance of breast cancer (MDA-MB-231), choriocarcinoma (JEG-3), and human lung fibroblast (MRC-5) cell line. According to IC50 values, all complexes exhibited a significantly stronger antiproliferative effect on tested cell lines compared to cisplatin. Due to reduced adverse effects on MRC-5 cells, the complex containing ethyl-substituent (10 μM) was selected for further examination with resveratrol (25 μM) cotreatment. Resveratrol enhanced the survival of MRC-5 cells while diminished the viability of both used cancer cell lines when applied combined with selected complex. Furthermore, cotreatment of these two compounds decreased the migratory potential of tested cancer cell lines. The examined platinum(IV) complex was able to induce oxidative stress in all tested cell lines. Resveratrol proved to be efficient in protecting MRC-5 cells from complex-induced oxidative damage, while it significantly amplified antiproliferative, antimigratory, and prooxidative effects of platinum(IV) complex on both examined cancer cell lines. These findings may be valuable in elucidating the mechanism of action of platinum(IV) drugs, which should be further investigated.