Collateral lethality occurs when loss of one paralog renders cancer cells dependent on the remaining paralog. Combining genome scale CRISPR/Cas9 screens coupled with RNA-sequencing in over 900 cancer cell lines, we found that cancers of nervous system lineage, including adult and pediatric gliomas and neuroblastomas, required the nuclear kinase Vaccinia-Related Kinase 1 (VRK1) for their survival. VRK1 dependency was inversely correlated with expression of its paralog VRK2. VRK2 knockout in VRK2-expressing cell lines sensitized cells to VRK1 knockout, and conversely, VRK2 overexpression increased cell fitness in VRK1-dependent cell lines upon suppression of VRK1. DNA methylation of the VRK2 promoter was associated with low VRK2 expression in human neuroblastomas, and adult and pediatric gliomas. Mechanistically, depletion of VRK1 reduced Barrier-to-Autointegration Factor (BAF) phosphorylation, induced abnormal chromosome segregation. and dysregulated nuclear membrane re-formation following mitosis, resulting in increased DNA damage and apoptosis. Together, these observations identify VRK1 as a synthetic lethal target in VRK2-methylated adult and pediatric gliomas and neuroblastomas.