TP53, a critical tumour suppressor gene, is mutated in over half of all cancers resulting in mutant-p53 protein accumulation and poor patient survival. Therapeutic strategies to target mutant-p53 cancers are urgently needed. We show that accumulated mutant-p53 protein suppresses the expression of SLC7A11, a component of the cystine/glutamate antiporter, system xC−, through binding to the master antioxidant transcription factor NRF2. This diminishes glutathione synthesis, rendering mutant-p53 tumours susceptible to oxidative damage. System xC− inhibitors specifically exploit this vulnerability to preferentially kill cancer cells with stabilized mutant-p53 protein. Moreover, we demonstrate that SLC7A11 expression is a novel and robust predictive biomarker for APR-246, a first-in-class mutant-p53 reactivator that also binds and depletes glutathione in tumours, triggering lipid peroxidative cell death. Importantly, system xC− antagonism strongly synergizes with APR-246 to induce apoptosis in mutant-p53 tumours. We propose a new paradigm for targeting cancers that accumulate mutant-p53 protein by inhibiting the SLC7A11–glutathione axis.