Reasoning processes have been closely associated with prefrontal cortex (PFC), but specifically emerge from interactions among networks of brain regions. Yet it remains a challenge to integrate these brain-wide interactions in identifying the flow of processing emerging from sensory brain regions to abstract processing regions, particularly within PFC. Functional magnetic resonance imaging data were collected while participants performed a visuo-spatial reasoning task. We found increasing involvement of occipital and parietal regions together with caudal-rostral recruitment of PFC as stimulus dimensions increased. Brain-wide connectivity analysis revealed that interactions between primary visual and parietal regions predominantly influenced activity in frontal lobes. Caudal-to-rostral influences were found within left-PFC. Right-PFC showed evidence of rostral-to-caudal connectivity in addition to relatively independent influences from occipito-parietal cortices. In the context of hierarchical views of PFC organization, our results suggest that a caudal-to-rostral flow of processing may emerge within PFC in reasoning tasks with minimal top-down deductive requirements.