Various paradigms can make visual stimuli disappear from awareness, but they often involve stimuli that are either relatively weak, competing with other salient inputs, and/or presented for a prolonged period of time. Here we explore a phenomenon that involves controlled perceptual disappearance of a peripheral visual stimulus without these limitations. It occurs when one eye's stimulus is abruptly removed during a binocular rivalry situation. This manipulation renders the remaining stimulus, which is still being presented to the other eye, invisible for up to several seconds. Our results suggest that this perceptual disappearance depends on a visual offset-transient that promotes dominance of the eye in which it occurs regardless of whether the eye is dominant or suppressed at the moment of the transient event. Using computational modeling, we demonstrate that standard rivalry mechanisms of interocular inhibition can indeed be complemented by a hypothesized transient-driven gating mechanism to explain the phenomenon. In essence, such a system suggests that visual awareness is dominated by the eye that receives transients and "sticks with" this eye-based dominance for some time in the absence of further transient events. We refer to this phenomenon as the "disrupted rivalry effect" and suggest that it is a potentially powerful paradigm for the study of cortical suppression mechanisms and the neural correlates of visual awareness.