Some individuals with autism spectrum (AS) perform better on visual reasoning tasks than would be predicted by their general cognitive performance. In individuals with AS, mechanisms in the brain's visual area that underlie visual processing play a more prominent role in visual reasoning tasks than they do in normal individuals. In addition, increased connectivity with the visual area is thought to be one of the neural bases of autistic visual cognitive abilities. However, the contribution of such brain connectivity to visual cognitive abilities is not well understood, particularly in children. In this study, we investigated how functional connectivity between the visual areas and higher-order regions, which is reflected by alpha, beta and gamma band oscillations, contributes to the performance of visual reasoning tasks in typically developing (TD) (n = 18) children and AS children (n = 18). Brain activity was measured using a custom child-sized magneto-encephalograph. Imaginary coherence analysis was used as a proxy to estimate the functional connectivity between the occipital and other areas of the brain. Stronger connectivity from the occipital area, as evidenced by higher imaginary coherence in the gamma band, was associated with higher performance in the AS children only. We observed no significant correlation between the alpha or beta bands imaginary coherence and performance in the both groups. Alpha and beta bands reflect top-down pathways, while gamma band oscillations reflect a bottom-up influence. Therefore, our results suggest that visual reasoning in AS children is at least partially based on an enhanced reliance on visual perception and increased bottom-up connectivity from the visual areas.