Chronic myeloid leukaemia (CML) arises after transformation of a haemopoietic stem cell (HSC) by the protein-tyrosine kinase BCR–ABL. Direct inhibition of BCR–ABL kinase has revolutionized disease management, but fails to eradicate leukaemic stem cells (LSCs), which maintain CML. LSCs are independent of BCR–ABL for survival, providing a rationale for identifying and targeting kinase-independent pathways. Here we show using proteomics, transcriptomics and network analyses that in human LSCs, aberrantly expressed proteins, in both imatinib-responder and non-responder patients, are modulated in concert with p53 (also known as TP53) and c-MYC regulation. Perturbation of both p53 and c-MYC, and not BCR–ABL itself, leads to synergistic cell kill, differentiation, and near elimination of transplantable human LSCs in mice, while sparing normal HSCs. This unbiased systems approach targeting connected nodes exemplifies a novel precision medicine strategy providing evidence that LSCs can be eradicated.