Neural oscillations in the gamma range are the dominant rhythmic activation pattern in the human auditory cortex. These gamma oscillations are functionally relevant for the processing of rapidly changing acoustic information in both speech and non-speech sounds. Accordingly, there is a tight link between the temporal resolution ability of the auditory system and inherent neural gamma oscillations. Transcranial random noise stimulation (tRNS) has been demonstrated to specifically increase gamma oscillation in the human auditory cortex. However, neither the physiological mechanisms of tRNS nor the behavioral consequences of this intervention are completely understood. In the present study we stimulated the human auditory cortex bilaterally with tRNS while EEG was continuously measured. Modulations in the participants' temporal and spectral resolution ability were investigated by means of a gap detection task and a pitch discrimination task. Compared to sham, auditory tRNS increased the detection rate for near-threshold stimuli in the temporal domain only, while no such effect was present for the discrimination of spectral features. Behavioral findings were paralleled by reduced peak latencies of the P50 and N1 component of the auditory event-related potentials (ERP) indicating an impact on early sensory processing. The facilitating effect of tRNS was limited to the processing of near-threshold stimuli while stimuli clearly below and above the individual perception threshold were not affected by tRNS. This non-linear relationship between the signal-to-noise level of the presented stimuli and the effect of stimulation further qualifies stochastic resonance (SR) as the underlying mechanism of tRNS on auditory processing. Our results demonstrate a tRNS related improvement in acoustic perception of time critical auditory information and, thus, provide further indices that auditory tRNS can amplify the resonance frequency of the auditory system.