The human brain entertains rich spatiotemporal dynamics, which are drastically reconfigured when consciousness is lost due to anaesthesia or disorders of consciousness (DOC). Here, we sought to identify the neurobiological mechanisms that explain how transient pharmacological intervention and chronic neuroanatomical injury can lead to common reconfigurations of neural activity. We developed and systematically perturbed a neurobiologically realistic model of whole-brain haemodynamic signals. By incorporating PET data about the cortical distribution of GABA receptors, our computational model reveals a key role of spatially-specific local inhibition for reproducing the functional MRI activity observed during anaesthesia with the GABA-ergic agent propofol. Additionally, incorporating diffusion MRI data obtained from DOC patients reveals that the dynamics that characterise loss of consciousness can also emerge from randomised neuroanatomical connectivity. Our results generalise between anaesthesia and DOC datasets, demonstrating how increased inhibition and connectome perturbation represent distinct neurobiological paths towards the characteristic activity of the unconscious brain.