Paclitaxel (PTX) is a chemotherapeutic agent affecting microtubule polymerization. The efficacy of PTX depends on the type of tumor, and its improvement would be beneficial in patients' treatment. Therefore, we tested the effect of slow sulfide donor GYY4137 on paclitaxel sensitivity in two different breast cancer cell lines, MDA-MB-231, derived from a triple negative cell line, and JIMT1, which overexpresses HER2 and is resistant to trastuzumab. In JIMT1 and MDA-MB-231 cells, we compared IC50 and some metabolic (apoptosis induction, lactate/pyruvate conversion, production of reactive oxygen species, etc.), morphologic (changes in cytoskeleton), and functional (migration, angiogenesis) parameters for PTX and PTX/GYY4137, aiming to determine the mechanism of the sensitization of PTX. We observed improved sensitivity to paclitaxel in the presence of GYY4137 in both cell lines, but also some differences in apoptosis induction and pyruvate/lactate conversion between these cells. In MDA-MB-231 cells, GYY4137 increased apoptosis without affecting the IP3R1 protein, changing the morphology of the cytoskeleton. A mechanism of PTX sensitization by GYY4137 in JIMT1 cells is distinct from MDA-MB-231, and remains to be further elucidated. We suggest different mechanisms of action for H2S on the paclitaxel treatment of MDA-MB-231 and JIMT1 breast cancer cell lines.