Binocular rivalry is a phenomenon in which perception spontaneously shifts between two different images that are dichoptically presented to the viewer. By elucidating the cortical networks responsible for these stochastic fluctuations in perception, we can potentially learn much about the neural correlates of visual awareness. We obtained concurrent EEG-fMRI data for a group of 20 healthy human subjects during the continuous presentation of dichoptic visual stimuli. The two eyes’ images were tagged with different temporal frequencies so that eye specific steady-state visual evoked potential (SSVEP) signals could be extracted from the EEG data for direct comparison with changes in fMRI BOLD activity associated with binocular rivalry. We additionally included a smooth replay condition that emulated the perceptual transitions experienced during binocular rivalry as a control stimulus. We evaluated a novel SSVEP-informed fMRI analysis in this study in order to delineate the temporal dynamics of rivalry-related BOLD activity from both an electrophysiological and behavioral perspective. In this manner, we assessed BOLD activity during rivalry that was directly correlated with peaks and crosses of the two rivaling, frequency-tagged SSVEP signals, for comparison with BOLD activity associated with subject reported perceptual transitions. Our findings point to a critical role of a right lateralized fronto-parietal network in the processing of bistable stimuli, given that BOLD activity in the right superior/inferior parietal lobules was significantly elevated throughout binocular rivalry and in particular during perceptual transitions, compared with the replay condition. Based on the SSVEP-informed analysis, rivalry was further associated with significantly enhanced BOLD suppression in the posterior mid-cingulate cortex during perceptual transitions, compared with SSVEP crosses. Overall, this work points to a careful interplay between early visual areas, the right posterior parietal cortex and the mid-cingulate cortex in mediating the spontaneous perceptual changes associated with binocular rivalry and has significant implications for future multimodal imaging studies of perception and awareness.