Abstract Directing and maintaining attention toward relevant information and away from non-relevant information is a critical competence of higher-order nervous systems. Here, we used directed connectivity to investigate how the human brain prioritizes appropriate processing paths when participants are performing a behavioral task requiring attention in the visual or the auditory modality. We show that the efficient transfer of information relevant for the task is mediated by a region- and task-specific decrease of alpha band connectivity from the parietal and, in case a motor response is required, motor cortex to the relevant sensory cortices. Further, alpha-band connectivity modulations reliably predict alpha power modulations in the task-related sensory cortices, particularly where the task-irrelevant cortex is inhibited via local alpha power increases. We suggest that the task- and region-specific modulation of alpha-band connectivity in the present study is a basic neuronal mechanism orchestrating the allocation of task-relevant neuronal resources related to and possibly underlying the previously reported sensory alpha power modulations in association with the allocation of competing attentional resources.