Ongoing fluctuations in neural excitability and connectivity influence whether or not a stimulus is seen. Do they also influence which stimulus is seen? We recorded magnetoencephalography data while 21 human participants viewed face or house stimuli, either one at a time or under bistable conditions induced through binocular rivalry. Multivariate pattern analysis revealed common neural substrates for rivalrous versus nonrivalrous stimuli with an additional delay of ∼36 msec for the bistable stimulus, and poststimulus signals were source-localized to the fusiform face area. Before stimulus onset followed by a face versus house report, fusiform face area showed stronger connectivity to primary visual cortex and to the rest of the cortex in the alpha frequency range (8–13 Hz), but there were no differences in local oscillatory alpha power. The prestimulus connectivity metrics predicted the accuracy of poststimulus decoding and the delay associated with rivalry disambiguation suggesting that perceptual content is shaped by ongoing neural network states.