The role of attention in creative cognition remains controversial. Neuroimaging studies have reported activation of brain regions linked to both cognitive control and spontaneous imaginative processes, raising questions about how these regions interact to support creative thought. Using functional magnetic resonance imaging (fMRI), we explored this question by examining dynamic interactions between brain regions during a divergent thinking task. Multivariate pattern analysis revealed a distributed network associated with divergent thinking, including several core hubs of the default (posterior cingulate) and executive (dorsolateral prefrontal cortex) networks. The resting-state network affiliation of these regions was confirmed using data from an independent sample of participants. Graph theory analysis assessed global efficiency of the divergent thinking network, and network efficiency was found to increase as a function of individual differences in divergent thinking ability. Moreover, temporal connectivity analysis revealed increased coupling between default and salience network regions (bilateral insula) at the beginning of the task, followed by increased coupling between default and executive network regions at later stages. Such dynamic coupling suggests that divergent thinking involves cooperation between brain networks linked to cognitive control and spontaneous thought, which may reflect focused internal attention and the top-down control of spontaneous cognition during creative idea production.