Cortical responses to sensory stimuli are strongly modulated by temporal context. One of the best studied examples of such modulation is sensory adaptation. We first show that in response to repeated tones pyramidal (Pyr) neurons in male mouse auditory cortex (A1) exhibit facilitating and stable responses, in addition to adapting responses. To examine the potential mechanisms underlying these distinct temporal profiles, we developed a reduced spiking model of sensory cortical circuits that incorporated the signature short-term synaptic plasticity (STP) profiles of the inhibitory parvalbumin (PV) and somatostatin (SST) interneurons. The model accounted for all three temporal response profiles as the result of dynamic changes in excitatory/inhibitory balance produced by STP, primarily through shifts in the relative latency of Pyr and inhibitory neurons. Transition between the three response profiles was possible by changing the strength of the inhibitory PVfiPyr and SSTfiPyr synapses. The model predicted that a unit's latency would be related to its temporal profile. Consistent with this prediction, the latency of stable units was significantly shorter than that of adapting and facilitating units. Furthermore, because of the history-dependence of STP the model generated a paradoxical prediction: that inactivation of inhibitory neurons during one tone would decrease the response of A1 neurons to a subsequent tone. Indeed, we observed that optogenetic inactivation of PV neurons during one tone counterintuitively decreased the spiking of Pyr neurons to a subsequent tone 400 ms later. These results provide evidence that STP is critical to temporal context-dependent responses in the sensory cortex.