Few therapies target the loss of tumor suppressor genes in cancer. We examine CRISPR-SpCas9 and RNA-interference loss-of-function screens to identify new therapeutic targets associated with genomic loss of tumor suppressor genes. The endosomal sorting complexes required for transport (ESCRT) ATPases VPS4A and VPS4B score as strong synthetic lethal dependencies. VPS4A is essential in cancers harboring loss of VPS4B adjacent to SMAD4 on chromosome 18q and VPS4B is required in tumors with co-deletion of VPS4A and CDH1 (E-cadherin) on chromosome 16q. We demonstrate that more than 30% of cancers selectively require VPS4A or VPS4B. VPS4A suppression in VPS4B-deficient cells selectively leads to ESCRT-III filament accumulation, cytokinesis defects, nuclear deformation, G2/M arrest, apoptosis, and potent tumor regression. CRISPR-SpCas9 screening and integrative genomic analysis reveal other ESCRT members, regulators of abscission, and interferon signaling as modifiers of VPS4A dependency. We describe a compendium of synthetic lethal vulnerabilities and nominate VPS4A and VPS4B as high-priority therapeutic targets for cancers with 18q or 16q loss.