General anesthetics work through a variety of molecular mechanisms while resulting in the common end point of sedation and loss of consciousness. Generally, the administration of common anesthetics induces reduction in synaptic excitation while promoting synaptic inhibition. Exogenous modulation of the anesthetics' synaptic effects can help determine the neuronal pathways involved in anesthesia. For example, both animal and human studies have shown that exogenously induced increases in acetylcholine in the brain can elicit wakeful-like behavior despite the continued presence of the anesthetic. However, the underlying mechanisms of anesthesia reversal at the cellular level have not been investigated. Here we apply a computational model of a network of excitatory and inhibitory neurons to simulate the network-wide effects of anesthesia, due to changes in synaptic inhibition and excitation, and their reversal by cholinergic activation through muscarinic receptors. We use a differential evolution algorithm to fit model parameters to match measures of spiking activity, neuronal connectivity, and network dynamics recorded in the visual cortex of rodents during anesthesia with desflurane in vivo. We find that facilitating muscarinic receptor effects of acetylcholine on top of anesthetic-induced synaptic changes predicts the reversal of anesthetic suppression of neurons' spiking activity, functional connectivity, as well as pairwise and population interactions. Thus, our model predicts a specific neuronal mechanism for the cholinergic reversal of anesthesia consistent with experimental behavioral observations.