Plasticity of the cell state has been proposed to drive resistance to multiple classes of cancer therapies, thereby limiting their effectiveness. A high-mesenchymal cell state observed in human tumors and cancer cell lines has been associated with resistance to multiple treatment modalities across diverse cancer lineages, but the mechanistic underpinning for this state has remained incompletely understood. Here we molecularly characterize this therapy-resistant high-mesenchymal cell state in human cancer cell lines and organoids and show that it depends on a druggable lipid-peroxidase pathway that protects against ferroptosis, a non-apoptotic form of cell death induced by the build-up of toxic lipid peroxides. We show that this cell state is characterized by activity of enzymes that promote the synthesis of polyunsaturated lipids. These lipids are the substrates for lipid peroxidation by lipoxygenase enzymes. This lipid metabolism creates a dependency on pathways converging on the phospholipid glutathione peroxidase (GPX4), a selenocysteine-containing enzyme that dissipates lipid peroxides and thereby prevents the iron-mediated reactions of peroxides that induce ferroptotic cell death. Dependency on GPX4 was found to exist across diverse therapy-resistant states characterized by high expression of ZEB1, including epithelial-mesenchymal transition in epithelial-derived carcinomas, TGFβ-mediated therapy-resistance in melanoma, treatment-induced neuroendocrine transdifferentiation in prostate cancer, and sarcomas, which are fixed in a mesenchymal state owing to their cells of origin. We identify vulnerability to ferroptic cell death induced by inhibition of a lipid peroxidase pathway as a feature of therapy-resistant cancer cells across diverse mesenchymal cell-state contexts.