Face perception is a vital part of human social interactions. The social value of faces makes their efficient detection evolutionarily advantageous. It has been suggested that this might occur nonconsciously, but experimental results are equivocal thus far. Here, we probe nonconscious face perception using a novel combination of binocular rivalry with continuous flash suppression and steady-state visually evoked potentials. In the first two experiments, participants viewed either non-face objects, neutral faces (Study 1), or fearful faces (Study 2). Consistent with the hypothesis that faces are processed nonconsciously, we found that faces broke through suppression faster than objects. We did not, however, observe a concomitant face-selective steady-state visually evoked potential. Study 3 was run to reconcile this paradox. We hypothesized that the faster breakthrough time was due to a mid-level visual feature, curvilinearity, rather than high-level category membership, which would explain the behavioral difference without neural evidence of face-selective processing. We tested this hypothesis by presenting participants with four different groups of stimuli outside of conscious awareness: rectilinear objects (e.g., chessboard), curvilinear objects (e.g., dartboard), faces, and objects that were not dominantly curvilinear or rectilinear. We found that faces and curvilinear objects broke through suppression faster than objects and rectilinear objects. Moreover, there was no difference between faces and curvilinear objects. These results support our hypothesis that the observed behavioral advantage for faces is due to their curvilinearity, rather than category membership.