In binocular rivalry (BR), sensory input remains the same yet subjective experience fluctuates irremediably between two mutually exclusive representations. We investigated the perceptual stabilization effect of an additional sound on the BR dynamics using speech stimuli known to involve robust audiovisual (AV) interactions at several cortical levels. Subjects sensitive to the McGurk effect were presented looping videos of rivaling faces uttering /aba/ and /aga/, respectively, while synchronously hearing the voice /aba/. They reported continuously the dominant percept, either observing passively or trying actively to promote one of the faces. The few studies that investigated the influence of information from an external modality on perceptual competition reported results that seem at first sight inconsistent. Since these differences could stem from how well the modalities matched, we addressed this by comparing two levels of AV congruence: real (/aba/ viseme) vs. illusory (/aga/ viseme producing the /ada/ McGurk fusion). First, adding the voice /aba/ stabilized both real and illusory congruent lips percept. Second, real congruence of the added voice improved volitional control whereas illusory congruence did not, suggesting a graded contribution to the top-down sensitivity control of selective attention. In conclusion, a congruent sound enhanced considerably attentional control over the perceptual outcome selection; however, differences between passive stabilization and active control according to AV congruency suggest these are governed by two distinct mechanisms. Based on existing theoretical models of BR, selective attention and AV interaction in speech perception, we provide a general interpretation of our findings.