Previous research suggests that default-mode network (DMN) and dorsal attention network (DAN) are involved in internally- and externally-directed attention, respectively, through interactions with salience network (SN) and frontoparietal network (FPCN). Performing a task requiring external attention is often accompanied by a down-regulation of attention to internal thoughts, and vice-versa. In contrast, we often divide our attention between the external environment and internal thoughts to pursue distinct goals, yet virtually no prior research has examined how brain networks support this functionally critical neurocognitive process. In the current study, participants planned their responses for an upcoming alternate uses divergent thinking task (AUT-Condition), indicated whether arrows were pointing left or right (Arrows-Condition) or performed both tasks simultaneously (Dual-Task condition). Behaviorally, the Dual-Task condition was associated with equivalent generation of alternate uses but increased RT variability compared to the single-task conditions. Static connectivity analyses indicated that FPCN and SN increased their connectivity to DMN and reduced their connectivity to DAN during the Dual-Task condition and the AUT-Condition compared to the Arrows-Condition. Furthermore, DAN-SN connectivity was highest during the Arrows-Condition, intermediate during the Dual-Task condition and lowest during the AUT-Condition. Finally, time-varying connectivity analyses indicated that individuals who reported spending less time thinking of alternate uses during the Dual-Task condition spent more time in a state associated with performing the Arrows-Condition. Overall, our results suggest that interactions between DMN, FPCN, SN and DAN allow internal-external dual-tasking, and that time-varying functional connectivity between these networks is sensitive to attentional fluctuations between tasks during dual-tasking.