It is not clear how, after a large perturbation, the brain explores the vast space of potential neuronal activity states to recover those compatible with consciousness. Here, we analyze recovery from pharmacologically induced coma to show that neuronal activity en route to consciousness is confined to a low-dimensional subspace. In this subspace, neuronal activity forms discrete metastable states persistent on the scale of minutes. The network of transitions that links these metastable states is structured such that some states form hubs that connect groups of otherwise disconnected states. Although many paths through the network are possible, to ultimately enter the activity state compatible with consciousness, the brain must first pass through these hubs in an orderly fashion. This organization of metastable states, along with dramatic dimensionality reduction, significantly simplifies the task of sampling the parameter space to recover the state consistent with wakefulness on a physiologically relevant timescale.