Constructive mechanisms in the auditory system may restore a fragmented sound when a gap in this sound is rendered inaudible by noise to yield a continuity illusion. Using combined psychoacoustic and electroencephalography experiments in humans, we found that the sensory-perceptual mechanisms that enable restoration suppress auditory cortical encoding of gaps in interrupted sounds. When physically interrupted tones are perceptually restored, stimulus-evoked synchronization of cortical oscillations at approximately 4 Hz is suppressed as if physically uninterrupted sounds were encoded. The restoration-specific suppression is induced most strongly in primary-like regions in the right auditory cortex during illusorily filled gaps and also shortly before and after these gaps. Our results reveal that spontaneous modulations in slow evoked auditory cortical oscillations that are involved in encoding acoustic boundaries may determine the perceived continuity of sounds in noise. Such fluctuations could facilitate stable hearing of fragmented sounds in natural environments.