The intrinsic organization of functional brain networks is known to change with age, and is affected by perceptual input and task conditions. Here, we compare functional activity and connectivity during music listening and rest between younger (N=24) and older (N=24) adults, using whole brain regression, seed-based connectivity, and ROI-ROI connectivity analyses. As expected, activity and connectivity of auditory and reward networks scaled with liking during music listening in both groups. Younger adults show higher within-network connectivity of auditory and reward regions as compared to older adults, both at rest and during music listening, but this age-related difference at rest was reduced during music listening, especially in individuals who self-report high musical reward. Furthermore, younger adults showed higher functional connectivity between auditory network and medial prefrontal cortex (mPFC) that was specific to music listening, whereas older adults showed a more globally diffuse pattern of connectivity, including higher connectivity between auditory regions and bilateral lingual and inferior frontal gyri. Finally, connectivity between auditory and reward regions was higher when listening to music selected by the participant. These results highlight the roles of aging and reward sensitivity on auditory and reward networks. Results may inform the design of music- based interventions for older adults, and improve our understanding of functional network dynamics of the brain at rest and during a cognitively engaging task.