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.