Recent advancements in computational learning techniques have enabled the estimation of brain age (BA) from neuroimaging data. The difference between chronological age (CA) and BA, known as the BA gap, can potentially serve as a biomarker of brain health. Studies, however, have documented low correlations between BA gap and cognition in healthy aging. This suggests that protective mechanisms in the brain may help counter the effect of accelerated brain aging. Here, we investigated whether redundancy in brain networks may protect cognitive function in individuals with accelerated brain aging. First, we employed deep learning to estimate individual brain ages from structural magnetic resonance imaging (MRI). Next, we associated CA, BA, and BA gap, with cognitive measures and network topology derived from diffusion MRI and tractography. We found that CA and BA were both similarly related to cognitive measures and network topology, while BA gap did not show strong relationships in either domain. Despite observing no strong relationships between brain-age gap (BA gap) and demographic variables, cognitive measures, or topological features in healthy aging, individuals with accelerated aging (BA gap+) exhibited lower average degree and redundancy within the dorsal attention network compared to those with delayed aging (BA gap-). Furthermore, redundancy in the dorsal attention network was positively associated with processing speed in BA gap+ individuals. These results indicate a potential neuroprotective role of redundancy in structural brain networks for mitigating the impact of accelerated brain atrophy on cognitive performance in healthy aging.