In older adults, cognitive resources play a key role in maintaining postural stability. In the present study, we evaluated whether increasing postural instability using sway referencing induces changes in resource allocation in dual-task performance leading older adults to prioritize the more age-salient posture task over a cognitive task. Young and older adults participated in the study which comprised two sessions. In the first session, three posture tasks (stable, sway reference visual, sway reference somatosensory) and a working memory task (n-back) were examined. In the second session, single- and dual-task performance of posture and memory were assessed. Postural stability improved with session. Participants were more unstable in the sway reference conditions, and pronounced age differences were observed in the somatosensory sway reference condition. In dual-task performance on the stable surface, older adults showed an almost 40% increase in instability compared to single-task. However, in the sway reference somatosensory condition, stability was the same in single- and dual-task performance, whereas pronounced (15%) costs emerged for cognition. These results show that during dual-tasking while standing on a stable surface, older adults have the flexibility to allow an increase in instability to accommodate cognitive task performance. However, when instability increases by means of compromising somatosensory information, levels of postural control are kept similar in single- and dual-task, by utilizing resources otherwise allocated to the cognitive task. This evidence emphasizes the flexible nature of resource allocation, developed over the life-span to compensate for age-related decline in sensorimotor and cognitive processing.