At the onset of metazoan cell division the nuclear envelope breaks down to enable capture of chromosomes by the microtubule-containing spindle apparatus. During anaphase, when chromosomes have separated, the nuclear envelope is reassembled around the forming daughter nuclei. How the nuclear envelope is sealed, and how this is coordinated with spindle disassembly, is largely unknown. Here we show that endosomal sorting complex required for transport (ESCRT)-III, previously found to promote membrane constriction and sealing during receptor sorting, virus budding, cytokinesis and plasma membrane repair, is transiently recruited to the reassembling nuclear envelope during late anaphase. ESCRT-III and its regulatory AAA (ATPase associated with diverse cellular activities) ATPase VPS4 are specifically recruited by the ESCRT-III-like protein CHMP7 to sites where the reforming nuclear envelope engulfs spindle microtubules. Subsequent association of another ESCRT-III-like protein, IST1, directly recruits the AAA ATPase spastin to sever microtubules. Disrupting spastin function impairs spindle disassembly and results in extended localization of ESCRT-III at the nuclear envelope. Interference with ESCRT-III functions in anaphase is accompanied by delayed microtubule disassembly, compromised nuclear integrity and the appearance of DNA damage foci in subsequent interphase. We propose that ESCRT-III, VPS4 and spastin cooperate to coordinate nuclear envelope sealing and spindle disassembly at nuclear envelope-microtubule intersection sites during mitotic exit to ensure nuclear integrity and genome safeguarding, with a striking mechanistic parallel to cytokinetic abscission.