Although healthy aging is associated with general cognitive decline, there is considerable variability in the extent to which cognitive functions decline or are preserved. Preserved cognitive function in the context of age-related neuroanatomical and functional changes, has been attributed to compensatory mechanisms. However, the existing sparse evidence is largely focused on functions associated with the frontal cortex, leaving open the question of how wider age-related brain changes relate to compensation. We evaluated relationships between age-related neural and functional changes in the context of preserved cognitive function by combining measures of structure, function, and cognitive performance during spoken language comprehension using a paradigm that does not involve an explicit task. We used a graph theoretical approach to derive cognitive activation-related functional magnetic resonance imaging networks. Correlating network properties with age, neuroanatomical variations, and behavioral data, we found that decreased gray matter integrity was associated with decreased connectivity within key language regions but increased overall functional connectivity. However, this network reorganization was less efficient, suggesting that engagement of a more distributed network in aging might be triggered by reduced connectivity within specialized networks.