Attentional influence over perception is particularly pronounced when sensory stimulation is ambiguous, where attention can reduce stimulus uncertainty and promote a stable interpretation of the world. However, binocular rivalry, an extensively studied visual ambiguity, has proved to be comparatively resistant to attentional modulation. We hypothesize that this apparent inconsistency reflects fluctuations in the degree of unresolved competition during binocular rivalry. Namely, attentional influence over rivalry dynamics should be limited to phases of relatively unresolved stimulus competition, such as ends of individual dominance periods. We found that transient, feature-based cues congruent with the dominant stimulus prolonged dominance durations, while cues matching the suppressed stimulus hastened its return to dominance. Notably, the effect of cues depended on when the cues are presented. Cues presented late, but not early, during a given episode of perceptual dominance influenced rivalry dynamics. This temporal pattern mirrors known changes in the relative competitive dynamics of rival stimuli, revealing that selective effects occur only during temporal windows containing weak resolution of visual competition. In conclusion, these findings reveal that unresolved competition, which gates attention across a variety of domains, is also crucial in determining the susceptibility of binocular rivalry to selective influences.