Neural activity fluctuates over time, creating considerable variability across trials. This trial-by-trial neural variability is dramatically reduced (“quenched”) after the presentation of sensory stimuli. Likewise, the power of neural oscillations, primarily in the alpha-beta band, is also reduced after stimulus onset. Despite their similarity, these phenomena have so far been studied and discussed independently. We hypothesized that the two phenomena are tightly coupled in electrophysiological recordings of large cortical neural populations. To test this, we examined magnetoencephalography (MEG) recordings of healthy subjects viewing repeated presentations of a visual stimulus. The timing, amplitude, and spatial topography of variability-quenching and power-suppression were remarkably similar. Neural variability quenching was eliminated by excluding the alpha-beta band from the recordings, but not by excluding other frequency-bands. Moreover, individual magnitudes of alpha-beta band-power explained 86% of between-subject differences in variability quenching. An alternative mechanism that may generate variability quenching is increased phase alignment across trials. However, changes in inter-trial-phase-coherence (ITPC) exhibited distinct timing and no correlations with the magnitude of variability quenching in individual participants. These results reveal that neural variability quenching is tightly coupled with stimulus-induced changes in the power of alpha-beta band oscillations, associating two phenomena that have so far been studied in isolation.