Acquired drug resistance prevents cancer therapies from achieving stable and complete responses1. Emerging evidence implicates a key role for non-mutational drug resistance mechanisms underlying the survival of residual cancer ‘persister’ cells2,3,4. The persister cell pool constitutes a reservoir from which drug-resistant tumours may emerge. Targeting persister cells therefore presents a therapeutic opportunity to impede tumour relapse5. We previously found that cancer cells in a high mesenchymal therapy-resistant cell state are dependent on the lipid hydroperoxidase GPX4 for survival6. Here we show that a similar therapy-resistant cell state underlies the behaviour of persister cells derived from a wide range of cancers and drug treatments. Consequently, we demonstrate that persister cells acquire a dependency on GPX4. Loss of GPX4 function results in selective persister cell ferroptotic deathin vitroand prevents tumour relapse in mice. These findings suggest that targeting of GPX4 may represent a therapeutic strategy to prevent acquired drug resistance.