Infants' speech perception abilities change through the first year of life, from broad sensitivity to a wide range of speech contrasts to becoming more finely attuned to their native language. What remains unclear, however, is how this perceptual change relates to brain responses to native language contrasts in terms of the functional specialization of the left and right hemispheres. Here, to elucidate the developmental changes in functional lateralization accompanying this perceptual change, we conducted two experiments on Japanese infants using Japanese lexical pitch–accent, which changes word meanings with the pitch pattern within words. In the first behavioral experiment, using visual habituation, we confirmed that infants at both 4 and 10 months have sensitivities to the lexical pitch–accent pattern change embedded in disyllabic words. In the second experiment, near-infrared spectroscopy was used to measure cortical hemodynamic responses in the left and right hemispheres to the same lexical pitch–accent pattern changes and their pure tone counterparts. We found that brain responses to the pitch change within words differed between 4- and 10-month-old infants in terms of functional lateralization: Left hemisphere dominance for the perception of the pitch change embedded in words was seen only in the 10-month-olds. These results suggest that the perceptual change in Japanese lexical pitch–accent may be related to a shift in functional lateralization from bilateral to left hemisphere dominance.