Two identical autonomous dynamical systems coupled in a master-slave configuration can exhibit anticipated synchronization (AS) if the slave also receives a delayed negative self-feedback. Recently, AS was shown to occur in systems of simplified neuron models, requiring the coupling of the neuronal membrane potential with its delayed value. However, this coupling has no obvious biological correlate. Here we replace the self-feedback by a canonical neuronal microcircuit with standard chemical synapses, where the delayed inhibition is provided by an interneuron. In this biologically plausible scenario, a smooth transition from delayed synchronization (DS) to AS typically occurs when the inhibitory synaptic conductance is increased. We also show that these results can be extend to larger populations and are robust against noise and neuronal variability. Moreover, we propose that AS between oscillatory populations can explain a counterintuitive phenomenon observed in local field potential (LFP) data acquired from cortical areas of monkeys.