Efforts to understand the functional architecture of the brain have consistently identified multiple overlapping large-scale neural networks that are observable across multiple states. Despite the ubiquity of these networks, it remains unclear how regions within these large-scale neural networks interact to orchestrate behavior. Here, we collected functional magnetic resonance imaging data from 188 human subjects who engaged in three cognitive tasks and a resting-state scan. Using multiple tasks and a large sample allowed us to use split-sample validations to test for replication of results. We parceled the task-rest pairs into functional networks using a probabilistic spatial independent components analysis. We examined changes in connectivity between task and rest states using dual-regression analysis, which quantifies voxelwise connectivity estimates for each network of interest while controlling for the influence of signals arising from other networks and artifacts. Our analyses revealed systematic state-dependent functional connectivity in one brain region: the precuneus. Specifically, task performance led to increased connectivity (compared to rest) between the precuneus and the left frontoparietal network (lFPN), whereas rest increased connectivity between the precuneus and the default-mode network (DMN). The absolute magnitude of this effect was greater for DMN, suggesting a heightened specialization for resting-state cognition. All results replicated within the two independent samples. Our results indicate that the precuneus plays a core role not only in DMN, but also more broadly through its engagement under a variety of processing states.