Background/Objectives: Triple-negative breast cancer (TNBC) is the most challenging molecular subtype of breast cancer (BC) in clinical practice, associated with a worse prognosis due to limited treatment strategies and its insensitivity to conventional drugs. Zinc is an important trace element for homeostasis, and its Schiff base metal complexes have shown promise in treating advanced tumors. In this study, four new heteroleptic Zn(II) complexes (1–4) with Schiff bases were synthesized, characterized, and evaluated for their activity in BC cells. Methods: Compounds were synthesized, characterized, and their crystal structures were determined. Biological activity was assessed using MTT, clonogenic, scratch wound healing, caspase 3 and 8 activity, qPCR, and chemosensitization assays. Results: The complexes exhibited cytotoxicity against MCF-7 (luminal BC), MDA-MB-453 (HER2-positive BC), and MDA-MB-231 (TNBC) cell lines, with IC₅₀ values ranging from 0.01 to 20 µM. Complex 4 showed reduced cytotoxicity toward non-tumor cell lines. This, complexation with Zn(II) increased the cytotoxicity of the ligands, a trend not observed for complexes 1–3. Due to its favorable profile, complex 4 was selected for further assays, in which it inhibited colony formation and the cell migration of TNBC cells in a dose-dependent manner. Furthermore, this compound induced cell death independently of caspases, decreasing the activity of caspase 8. Interestingly, complex 4 sensitized TBNC cells to doxorubicin and paclitaxel, possibly modulating the epithelial–mesenchymal transition mechanism, as evidenced by increased CDH1 expression. Conclusions: Results suggest the potential of complex 4 in sensitizing aggressive BC cells to chemotherapy, proving to be a promising alternative in cases of therapeutic failure.