Acquired resistance to cancer drug therapies almost always occurs in advanced-stage patients even following a significant response to treatment. In addition to mutational mechanisms, various non-mutational resistance mechanisms have now been recognized. We previously described a chromatin-mediated subpopulation of reversibly drug-tolerant persisters that is dynamically maintained within a wide variety of tumour cell populations. Here we explore a potential role for microRNAs in such transient drug tolerance. Functional screening of 879 human microRNAs reveals miR-371-3p as a potent suppressor of drug tolerance. We identify PRDX6 (peroxiredoxin 6) as a key target of miR-371-3p in establishing drug tolerance by regulating PLA2/PKCα activity and reactive oxygen species. PRDX6 expression is associated with poor prognosis in cancers of multiple tissue origins. These findings implicate miR-371-3p as a suppressor of PRDX6 and suggest that co-targeting of peroxiredoxin 6 or modulating miR-371-3p expression together with targeted cancer therapies may delay or prevent acquired drug resistance.