In cancer, the tumour suppressor gene TP53 undergoes frequent missense mutations that endow mutant p53 proteins with oncogenic properties. Until now, a universal mutant p53 gain-of-function program has not been defined. By means of multi-omics: proteome, DNA interactome (chromatin immunoprecipitation followed by sequencing) and transcriptome (RNA sequencing/microarray) analyses, we identified the proteasome machinery as a common target of p53 missense mutants. The mutant p53–proteasome axis globally affects protein homeostasis, inhibiting multiple tumour-suppressive pathways, including the anti-oncogenic KSRP–microRNA pathway. In cancer cells, p53 missense mutants cooperate with Nrf2 (NFE2L2) to activate proteasome gene transcription, resulting in resistance to the proteasome inhibitor carfilzomib. Combining the mutant p53-inactivating agent APR-246 (PRIMA-1MET) with the proteasome inhibitor carfilzomib is effective in overcoming chemoresistance in triple-negative breast cancer cells, creating a therapeutic opportunity for treatment of solid tumours and metastasis with mutant p53.