Attentional control is crucial for selectively attending to relevant information when our brain is confronted with a multitude of sensory signals. Graph-theoretical measures provide a powerful tool for investigating the efficiency of brain network communication in separating and integrating information. Albeit, it has been demonstrated that anodal transcranial direct current stimulation (atDCS) can boost auditory attention in situations with high control demands, its effect on neurophysiological mechanisms of functional brain network communication in situations when attentional focus conflicts with perceptual saliency remain unclear. This study investigated the effects of atDCS on network connectivity and θ-oscillatory power under different levels of attentional-perceptual conflict. We hypothesized that the benefit of atDCS on network communication efficiency would be particularly apparent in conditions requiring high attentional control. Thirty young adults participated in a dichotic listening task with intensity manipulation, while EEG activity was recorded. In a cross-over design, participants underwent right frontal atDCS and sham stimulations in two separate sessions. Time-frequency decomposition and graph-theoretical analyses of network efficiency (using “small-world” properties) were used to quantify θ-oscillatory power and brain network efficiency, respectively. The atDCS-induced effect on task efficiency in the most demanding condition was mirrored only by an increase in network efficiency during atDCS compared with the sham stimulation. These findings are corroborated by Bayesian analyses. AtDCS-induced performance enhancement under high levels of attentional-perceptual conflicts is accompanied by an increase in network efficiency. Graph-theoretical measures can serve as a metric to quantify the effects of noninvasive brain stimulation on the separation and integration of information in the brain.