Prefrontal anodal transcranial direct current stimulation (tDCS) has been proposed as a potential approach to improve inhibitory control performance. The functional consequences of tDCS during inhibition tasks remain, however, largely unresolved. We addressed this question by analyzing functional magnetic resonance imaging (fMRI) recorded while participants completed a Go/NoGo task after right-lateralized prefrontal anodal tDCS with a crossover, sham-controlled, double-blind experimental design. We replicated previous evidence for an absence of offline effect of anodal stimulation on Go/NoGo performance. The fMRI results revealed a larger increase in right ventrolateral prefrontal activity for Go than NoGo trials in the anodal than sham condition. This pattern suggests that tDCS-induced increases in cortical excitability have larger effects on fMRI activity in regions with a lower task-related engagement. This was the case for the right prefrontal cortex in the Go condition in our task because while reactive inhibition was not engaged during execution trials, the unpredictability of the demand for inhibitory control still incited an engagement of proactive inhibition. Exploratory analyses further revealed that right prefrontal stimulation interacted with task-related functional demands in the supplementary motor area and the thalamus. Our collective results emphasize the dependency of offline tDCS functional effects on the task-related engagement of the stimulated areas and suggest that this factor might partly account for the discrepancies in the functional effects of tDCS observed in previous studies.