Inhibitory neurons in the cortex are highly diverse in terms of anatomy, electrophysiology and functions. In the mouse cortex, three major classes of interneurons expressing parvalbumin (PV), somatostatin (SST) and vasoactive intestinal peptide (VIP) constitute more than 80% of GABAergic interneurons. Together with excitatory (E) neurons, they form a canonical microcircuit relevant for cortical computations. Multiple experimental studies have revealed that this canonical microcircuit can exhibit counterintuitive nonlinear behavior. More specifically, the circuit can perform response reversal whereby depending on the presence of visual input, top-down modulation via VIP affects SST response oppositely (Fu et al., 2014; Pakan et al., 2016). Recent computational work has showed that static networks with nonlinear neuronal input-output functions can generate response reversal (del Molino et al., 2017). Yet, whether neuronal nonlinearities underlie these computations in the cortex is contentious (van Vreeswijk and Sompolinsky, 1998; Ahmadian and Miller, 2021). In contrast to static synapses widely assumed in computational studies, synapses in the brain are subject to short-term plasticity (STP) on a time scale of milliseconds to seconds. In particular, inhibitory synapses exhibit more pronounced short-term dynamics than excitatory synapses (Campagnola et al., 2021). How these experimentally identified short-term plasticity mechanisms shape network dynamics and the above mentioned computations is largely unknown. Here, we demonstrate that inhibitory short-term plasticity enables response reversal without the requirement for neuronal nonlinearities. We further identified that PV-to-E short-term depression provides the dominant influence on response reversal over other STP mechanisms. By examining the relationship between response reversal and inhibition stabilization, we found that PV stabilization is neither a necessary nor sufficient condition to have response reversal, whereas SST stabilization is a necessary but not sufficient condition to have response reversal. In summary, inhibitory short-term plasticity enables the network to perform nonlinear computations, allowing us to make experimentally testable predictions.