Considerable individual differences are widely observed in the sensitivity to opioid analgesics. We focused on rs12496846, rs698705, and rs10052295 single-nucleotide polymorphisms (SNPs) in the C3orf20, SLC8A2, and CTNND2 gene regions that we previously identified as possibly associated with postoperative analgesia after orthognathic surgery. We investigated associations between these SNPs and postoperative analgesia in 112 patients who underwent major open abdominal surgery in hospitals and were treated with analgesics, including opioids, after surgery. Total genomic DNA was extracted from peripheral blood or oral mucosa samples for genotyping each SNP. Effects of these potent SNPs on gene expression in the brain were also investigated in samples that were provided by the Stanley Foundation Brain Bank. In the association studies, carriers of the G allele of the rs12496846 SNP in the C3orf20 gene region were significantly associated with greater 24 h postoperative analgesic requirements among the three SNPs that were investigated (p = 0.0015), which corroborated a previous study of orthognathic patients (p < 0.0001). In the gene expression analysis, carriers of the G allele of the rs12496846 SNP were significantly associated with lower mRNA expression of the C3orf20 gene (p < 0.0001). These results indicate that this SNP could serve as a marker that predicts analgesic requirements.