Anesthesia induces a reconfiguration of the repertoire of functional brain states leading to a high function-structure similarity. However, it is unclear how these functional changes lead to loss of consciousness. Here we suggest that the mechanism of conscious access is related to a general dynamical rearrangement of the intrinsic hierarchical organization of the cortex. To measure cortical hierarchy, we applied the Intrinsic Ignition analysis to resting-state fMRI data acquired in awake and anesthetized macaques. Our results reveal the existence of spatial and temporal hierarchical differences of neural activity within the macaque cortex, with a strong modulation by the depth of anesthesia and the employed anesthetic agent. Higher values of Intrinsic Ignition correspond to rich and flexible brain dynamics whereas lower values correspond to poor and rigid, structurally driven brain dynamics. Moreover, spatial and temporal hierarchical dimensions are disrupted in a different manner, involving different hierarchical brain networks. All together suggest that disruption of brain hierarchy is a new signature of consciousness loss.