Cognition involves locally segregated and globally integrated processing. This process is hierarchically organized and linked to evidence from hierarchical modules in brain networks. However, researchers have not clearly determined how flexible transitions between these hierarchical processes are associated with cognitive performance. Here, we designed a multisource interference task (MSIT) and introduced the nested-spectral partition (NSP) method to detect hierarchical modules in brain functional networks. By defining hierarchical segregation and integration across multiple levels, we showed that the MSIT requires higher network segregation in the whole brain and most functional systems but generates higher integration in the control system. Meanwhile, brain networks have more flexible transitions between segregated and integrated configurations in the task state. Crucially, higher functional flexibility in the resting state, less flexibility in the task state and more efficient switching of the brain from resting to task states were associated with better task performance. Our hierarchical modular analysis was more effective at detecting alterations in functional organization and the phenotype of cognitive performance than graph-based network measures at a single level.