Some sources report a connection of cellular senescence with chronic pathological conditions; however, the association between particular cellular processes and general health is rarely examined. This study aims to test the relationship of general health with DNA damage pathways that play a crucial role in senescence. The association of ten selected SNPs with subjective and objective general health and functional ability indicators has been tested in 314 oldest-old people from Croatia. Multivariate logistic regression was employed to simultaneously test the impact of variables potentially influencing targeted health and functional ability variables. The best model, explaining 37.1% of the variance, has six independent significant predictors of functional ability scores: rs16847897 in TERC, rs533984 in MRE11A, and rs4977756 in CDKN2B, chronic disease count, Mini-Mental State Examination scores, and age at surveying. In conclusion, the examined ten loci involved in DNA damage repair pathways showed a more significant association with self-rated health and functional ability than with the number of disease or prescribed medicaments. The more frequent, longevity-related homozygote (GG) in rs16847897 was associated with all three aspects of self-assessments—health, mobility, and independence—indicating that this TERC locus might have a true impact on the overall vitality of the oldest-old persons.