Incomplete DNA replication and chromosome breakage during mitosis pose major threats to chromosome segregation. The CIP2A-TOPBP1 complex acts to mitigate this peril, but its exact role is not yet understood. Here, we report that DDIAS acts as a DNA-binding effector of the CIP2A-TOPBP1 complex. DDIAS directly interacts with TOPBP1 and the disruption of this interaction or inactivation of its single-stranded DNA (ssDNA)-binding ability impairs genome integrity and causes synthetic lethality with BRCA1 and BRCA2 deficiency. DDIAS does not promote the putative end-tethering function of CIP2A-TOPBP1 but rather acts to suppress ssDNA during mitosis. This role is emphasized by a pronounced genetic interaction between the genes coding for DDIAS and DNA polymerase zeta;. We conclude that DDIAS defines a mitotic DNA damage response that mitigates the threat of mitotic ssDNA arising from DNA replication stress, which we infer is a liability to accurate chromosome segregation.