(1) Malignant melanomas are dangerous skin cancers, and the treatment of melanomas with various cytostatic drugs often causes side effects and after their prolonged use resistance to these drugs appears. The aim of this study was to evaluate the anticancer effects of esculetin (a simple coumarin) and to assess pharmacodynamic interactions between esculetin and six commonly used cytostatic drugs (cisplatin, epirubicin, docetaxel, paclitaxel, mitoxantrone and vemurafenib) using an isobolographic analysis. (2) The experiments were carried out on four human malignant melanoma cell lines (FM55P, A375, FM55M2 and SK-MEL28). The effects of esculetin on viability, cell proliferation and cytotoxicity were verified in the range of concentrations of 2–200 μM. (3) Esculetin inhibited, in a dose-dependent manner, malignant melanoma cell viability and proliferation. The IC50for esculetin ranged from 18.20 ± 2.93 to 120.64 ± 30.39 μM depending on the melanoma cell lines used. The combinations of esculetin with epirubicin and vemurafenib showed antagonistic interactions, the combinations of esculetin with cisplatin, docetaxel and paclitaxel showed additive interactions. For the combinations of esculetin with mitoxantrone, the isobolographic analysis displayed synergy. (4) In the treatment of malignant melanoma, esculetin should not be combined with epirubicin or vemurafenib, due to the reduction of their anticancer effects, while the synergistic interactions (esculetin + mitoxantrone) deserve a preclinical recommendation as a beneficial combination during anticancer therapy.