A classical model of human attention holds that independent neural networks realize stimulus-driven reorienting and executive control of attention. Questioning full independence, the two functions do, however, engage overlapping networks with activations in cingulo-opercular regions such as anterior insula (AI) and a reverse pattern of activation (stimulus-driven reorienting), and deactivation (executive control) in temporoparietal junction (TPJ). To test for independent versus shared neural mechanisms underlying stimulus-driven and executive control of attention, we used fMRI and a task that isolates individual from concurrent demands in both functions. Results revealed super-additive increases of left AI activity and behavioral response costs under concurrent demands, suggesting a common bottleneck for stimulus-driven reorienting and executive control of attention. These increases were mirrored by non-additive decreases of activity in the default mode network (DMN), including posterior TPJ, regions where activity increased with off-task processes. The deactivations in posterior TPJ were spatially separated from stimulus-driven reorienting related activation in anterior TPJ, a differentiation that replicated in task-free resting state. Furthermore, functional connectivity indicated inhibitory coupling between posterior TPJ and AI during concurrent attention demands. These results demonstrate a role of AI in stimulus-driven and executive control of attention that involves down-regulation of internally directed processes in DMN.