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Decrease in cognitive performance after sleep deprivation followed by recovery after sleep suggests its key role, and especially non-rapid eye movement (NREM) sleep, in the maintenance of cognition. It remains unknown whether brain network reorganization in NREM sleep stages N2 and N3 can uniquely be mapped onto individual differences in cognitive performance after a recovery nap following sleep deprivation. Using resting state functional magnetic resonance imaging (fMRI), we quantified the integration and segregation of brain networks during NREM sleep stages N2 and N3 while participants took a 1-hour nap following 24-hour sleep deprivation, compared to well-rested wakefulness. Here, we advance a new analytic framework called the hierarchical segregation index (HSI) to quantify network segregation across spatial scales, from whole-brain to the voxel level, by identifying spatio-temporally overlapping large-scale networks and the corresponding voxel-to-region hierarchy. Our results show that network segregation increased in the default mode, dorsal attention and somatomotor networks during NREM sleep compared to wakefulness. Segregation within the visual, limbic, and executive control networks exhibited N2 versus N3 sleep-specific voxel-level patterns. More segregation during N3 was associated with worse recovery of working memory, executive attention, and psychomotor vigilance after the nap. The level of spatial resolution of network segregation varied among brain regions and was associated with the recovery of performance in distinct cognitive tasks. We demonstrated the sensitivity and reliability of voxel-level HSI to provide key insights into within-region variation, suggesting a mechanistic understanding of how NREM sleep replenishes cognition after sleep deprivation.