Sensory cortices must flexibly adapt their operations to internal states and external requirements. Sustained modulation of activity levels in different inhibitory interneuron populations may provide network-level mechanisms for adjustment of sensory cortical processing on behaviorally relevant timescales. However, understanding of the computational roles of inhibitory interneuron modulation has mostly been restricted to effects at short timescales, through the use of phasic optogenetic activation and transient stimuli. Here, we investigated how modulation of inhibitory interneurons affects cortical computation on longer timescales, by using sustained, network-wide optogenetic activation of parvalbumin-positive interneurons (the largest class of cortical inhibitory interneurons) to study modulation of auditory cortical responses to prolonged and naturalistic as well as transient stimuli. We found highly conserved spectral and temporal tuning in auditory cortical neurons, despite a profound reduction in overall network activity. This reduction was predominantly divisive, and consistent across simple, complex, and naturalistic stimuli. A recurrent network model with power-law input-output functions replicated our results. We conclude that modulation of parvalbumin-positive interneurons on timescales typical of sustained neuromodulation may provide a means for robust divisive gain control conserving stimulus representations.