We report that the marmoset, a 300-gram simian primate with a flat cortex, performs a challenging high-level perceptual task in a strikingly human-like manner. Across the same set of 400 images, marmosets' image-by-image core object recognition behavior was highly similar to that of humans -- and was nearly as human-like as was macaques' (r=0.73 vs. r=0.77). Separately, we found that marmosets' visual abilities far outstripped those of rodents -- marmosets substantially outperformed rats and generalized in a far more robust manner across images. Thus, core aspects of visual perception are conserved across simian primates, and marmosets may be a powerful small model organism for high-level visual neuroscience.