Cognitively demanding goal-directed tasks in the human brain are thought to involve the dynamic interplay of several large-scale neural networks, including the default-mode network (DMN), salience network (SN), and central-executive network (CEN). Resting-state functional magnetic resonance imaging (rsfMRI) studies have consistently shown that the CEN and SN negatively regulate activity in the DMN, and this switching is argued to be controlled by the right anterior insula (rAI) of the SN. However, what remains to be investigated is the pattern of directed network interactions during difficult perceptual decision-making tasks. We recorded fMRI data while participants categorized the left-right motion of moving dots. We defined regions of interest, extracted fMRI time series, and performed directed connectivity analysis using Granger causality techniques. Our analyses demonstrated that the slow oscillation (0.07-0.19 Hz) mediated the interactions within and between the DMN, SN, and CEN nodes both for easier and harder decision-making tasks. We found that the rAI, a key node of the SN, played a causal control over the DMN and CEN for easier decision-making tasks. The combined effort of the rAI and dorsal anterior cingulate cortex of the SN had the causal control over the DMN and CEN for a harder task. These findings provide important insights into how a sensory signal organizes among the DMN, SN, and CEN during sensory information-guided, goal-directed tasks.