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Two identical autonomous dynamical systems unidirectionally coupled in a sender-receiver configuration can exhibit anticipated synchronization (AS) if the receiver neuron also receives a delayed negative self-feedback. Recently, AS was shown to occur in a three-neuron motif with standard chemical synapses where the delayed inhibition was provided by an interneuron. Here, we show that a two-neuron model in the presence of an inhibitory autapse, which is a massive self-innervation present in the cortical architecture, may present AS. The GABAergic autapse regulates the internal dynamics of the receiver neuron and acts as the negative delayed self-feedback required by dynamical systems in order to exhibit AS. In this biologically plausible scenario, a smooth transition from the usual delayed synchronization (DS) to AS typically occurs when the inhibitory conductance is increased. The phenomenon is shown to be robust when model parameters are varied within a physiological range. For extremely large values of the inhibitory autapse the system undergoes to a phase-drift regime in which the receiver is faster than the sender. Furthermore, we show that the inhibitory autapse promotes a faster internal dynamics of the free-running Receiver when the two neurons are uncoupled, which could be the mechanism underlying anticipated synchronization and the DS-AS transition.