Female breast cancer is the most deadly cancer in women worldwide. The triple-negative breast cancer subtype therapies, due to the lack of specific drug targets, are still based on systemic chemotherapy with doxorubicin, which is burdened with severe adverse effects. To enhance therapeutic success and protect against systemic toxicity, drug carriers or combination therapy are being developed. Thus, an innovative liposomal formulation containing doxorubicin and the main nutraceutical, sulforaphane, has been developed. The anticancer efficacy and safety of the proposed liposomal formulation was evaluated in vivo, in a 4T1 mouse model of triple-negative breast cancer, and the mechanism of action was determined in vitro, using triple-negative breast cancer MDA-MB-231 and non-tumorigenic breast MCF-10A cell line. The elaborated drug carriers were shown to efficiently deliver both compounds into the cancer cell and direct doxorubicin to the cell nucleus. Incorporation of sulforaphane resulted in a twofold inhibition of tumor growth and the potential of up to a fourfold reduction in doxorubicin concentration due to the synergistic interaction between the two compounds. Sulforaphane was shown to increase the accumulation of doxorubicin in the nuclei of cancer cells, accompanied by inhibition of mitosis, without affecting the reactive oxygen species status of the cell. In normal cells, an antagonistic effect resulting in less cytotoxicity was observed. In vivo results showed that sulforaphane incorporation yielded not only cardioprotective, but also nephro- and hepatoprotective effects. The results of the research revealed the prospects of applying sulforaphane as a component of liposomal doxorubicin in triple-negative breast cancer chemotherapy.