Despite the association between cognitive impairment and delirium, little is known about whether genetic differences that confer cognitive resilience also confer resistance to delirium. To investigate whether older adults without postoperative delirium, compared with those with postoperative delirium, are more likely to have specific single nucleotide polymorphisms (SNPs) in the FKBP5, KIBRA, KLOTHO, MTNR1B, and SIRT1 genes known to be associated with cognition or delirium. This prospective nested matched exploratory case–control study included 94 older adults who underwent orthopedic surgery and screened for postoperative delirium. Forty-seven subjects had incident delirium, and 47 age-matched controls were not delirious. The primary study outcome was genotype frequency for the five SNPs. Compared with participants with delirium, those without delirium had higher adjusted odds of KIBRA SNP rs17070145 CT/TT [vs. CC; adjusted odds ratio (aOR) 2.80, 95% confidence interval (CI) 1.03, 7.54; p = 0.04] and MTNR1B SNP rs10830963 CG/GG (vs. CC; aOR 4.14, 95% CI 1.36, 12.59; p = 0.01). FKBP5 SNP rs1360780 CT/TT (vs. CC) demonstrated borderline increased adjusted odds of not developing delirium (aOR 2.51, 95% CI 1.00, 7.34; p = 0.05). Our results highlight the relevance of KIBRA, MTNR1B, and FKBP5 in understanding the complex relationship between delirium, cognition, and sleep, which warrant further study in larger, more diverse populations.