Cognitively demanding tasks that evoke activation in the brain's central-executive network (CEN) have been consistently shown to evoke decreased activation (deactivation) in the default-mode network (DMN). The neural mechanisms underlying this switch between activation and deactivation of large-scale brain networks remain completely unknown. Here, we use functional magnetic resonance imaging (fMRI) to investigate the mechanisms underlying switching of brain networks in three different experiments. We first examined this switching process in an auditory event segmentation task. We observed significant activation of the CEN and deactivation of the DMN, along with activation of a third network comprising the right fronto-insular cortex (rFIC) and anterior cingulate cortex (ACC), when participants perceived salient auditory event boundaries. Using chronometric techniques and Granger causality analysis, we show that the rFIC-ACC network, and the rFIC, in particular, plays a critical and causal role in switching between the CEN and the DMN. We replicated this causal connectivity pattern in two additional experiments: (i) a visual attention "oddball" task and (ii) a task-free resting state. These results indicate that the rFIC is likely to play a major role in switching between distinct brain networks across task paradigms and stimulus modalities. Our findings have important implications for a unified view of network mechanisms underlying both exogenous and endogenous cognitive control.