Anatomical and functional brain studies have converged to the hypothesis that autism spectrum disorders (ASD) are associated with atypical connectivity. Using a modified resting-state paradigm to drive subjects' attention, we provide evidence of a very marked interaction between ASD brain functional connectivity and cognitive state. We show that functional connectivity changes in opposite ways in ASD and typicals as attention shifts from external world towards one's body generated information. Furthermore, ASD subject alter more markedly than typicals their connectivity across cognitive states. Using differences in brain connectivity across conditions, we ranked brain regions according to their classification power. Anterior insula and dorsal-anterior cingulate cortex were the regions that better characterize ASD differences with typical subjects across conditions, and this effect was modulated by ASD severity. These results pave the path for diagnosis of mental pathologies based on functional brain networks obtained from a library of mental states. (Contains 9 figures and 1 table.)