Histone H3K36 trimethylation (H3K36me3) is frequently lost in multiple cancer types, identifying it as an important therapeutic target. We have identified a synthetic lethal interaction in which H3K36me3-deficient cancers are acutely sensitive to WEE1 inhibition. We show that RRM2, a ribonucleotide reductase subunit, is the target of this synthetic lethal interaction. RRM2 is regulated by two pathways in this context: first, H3K36me3 facilitates RRM2 expression; second, WEE1 inhibition degrades RRM2 through untimely CDK activation. Accordingly, WEE1 inhibition in H3K36me3-deficient cells results in RRM2 reduction, critical dNTP depletion, S-phase arrest and apoptosis. Consistent with these findings, the synthetic lethality can be suppressed by increasing RRM2 expression or inhibiting RRM2 degradation. We further demonstrate that WEE1 inhibitor AZD1775 regresses H3K36me3-deficient tumor xenografts. We have developed a biomarker to detect loss of H3K36me3, thus facilitating patient selection. As AZD1775 is already in Phase 2 clinical trials, we anticipate that these findings will be of clinical relevance.