"Neural inertia" is the brain's tendency to resist changes in its arousal state: it is manifested as emergence from anaesthesia occurring at lower drug doses than those required for anaesthetic induction, a phenomenon observed across very different species, from invertebrates to mammals. However, the brain is also subject to another form of inertia, familiar to most people: sleep inertia, the feeling of grogginess, confusion and impaired performance that typically follows awakening. Here, we propose a novel account of neural inertia, as the result of sleep inertia taking place after the artificial sleep induced by anaesthetics. We argue that the orexinergic and noradrenergic systems may be key mechanisms for the control of these transition states, with the orexinergic system exerting a stabilising effect through the noradrenergic system. This effect may be reflected at the macroscale in terms of altered functional anticorrelations between default mode and executive control networks of the human brain. The hypothesised link between neural inertia and sleep inertia could explain why different anaesthetic drugs induce different levels of neural inertia, and why elderly individuals and narcoleptic patients are more susceptible to neural inertia. This novel hypothesis also enables us to generate several empirically testable predictions at both the behavioural and neural levels, with potential implications for clinical practice.