The emergence of resistance to poly-ADP-ribose polymerase inhibitors (PARPi) poses a threat to the treatment of BRCA1 and BRCA2 (BRCA1/2)-deficient tumours. Stabilization of stalled DNA replication forks is a recently identified PARPi-resistance mechanism that promotes genomic stability in BRCA1/2-deficient cancers. Dissecting the molecular pathways controlling genomic stability at stalled forks is critical. Here we show that EZH2 localizes at stalled forks where it methylates Lys27 on histone 3 (H3K27me3), mediating recruitment of the MUS81 nuclease. Low EZH2 levels reduce H3K27 methylation, prevent MUS81 recruitment at stalled forks and cause fork stabilization. As a consequence, loss of function of the EZH2/MUS81 axis promotes PARPi resistance in BRCA2-deficient cells. Accordingly, low EZH2 or MUS81 expression levels predict chemoresistance and poor outcome in patients with BRCA2-mutated tumours. Moreover, inhibition of Ezh2 in a murine Brca2^−/− breast tumour model is associated with acquired PARPi resistance. Our findings identify EZH2 as a critical regulator of genomic stability at stalled forks that couples histone modifications to nuclease recruitment. Our data identify EZH2 expression as a biomarker of BRCA2-deficient tumour response to chemotherapy.