Spoken language perception may be constrained by a listener's cognitive resources, including verbal working memory (WM) capacity and basic auditory perception mechanisms. For Japanese listeners, it is unknown how, or even if, these resources are involved in the processing of pitch accent at the word level. The present study examined the extent to which native Japanese speakers could make correctness judgments on and categorize spoken Japanese words by pitch accent pattern, and how verbal WM capacity and acoustic pitch sensitivity related to perception ability. Results showed that Japanese listeners were highly accurate at judging pitch accent correctness (M = 93%), but that the more cognitively demanding accent categorization task yielded notably lower performance (M = 61%). Of chief interest was the finding that acoustic pitch sensitivity significantly predicted accuracy scores on both perception tasks, while verbal WM had a predictive role only for the categorization of a specific accent pattern. These results indicate first, that task demands greatly influence accuracy and second, that basic cognitive capacities continue to support perception of lexical prosody even in adult listeners.