Free energy perturbation (FEP) calculations can predict relative binding affinities of an antigen and its point mutants to the same human leukocyte antigen (HLA) with high accuracy (e.g., within 1.0 kcal/mol to experiment); however, a more challenging task is to compare binding affinities of wholly different antigens binding to completely different HLAs using FEP. Researchers have used a variety of different FEP schemes to compute and compare absolute binding affinities, with varied success. Here, we propose and assess a unifying scheme to compute the relative binding affinities of different antigens binding to completely different HLAs using absolute binding affinity FEP calculations. We apply our affinity calculation technique to HLA–antigen–T-cell receptor (TCR) systems relevant to celiac disease (CeD) by investigating binding affinity differences between HLA–DQ2.5 (enhanced CeD risk) and HLA–DQ7.5 (CeD protective) in the binary (HLA–gliadin) and ternary (HLA–gliadin–TCR) binding complexes for three gliadin derived epitopes: glia-α1, glia-α2, and glia-ω1. Based on FEP calculations with our carefully designed thermodynamic cycles, we demonstrate that HLA–DQ2.5 has higher binding affinity than HLA–DQ7.5 for gliadin and enhanced binding affinity with a common TCR, agreeing with known results that the HLA–DQ2.5 serotype exhibits increased risk for CeD. Our findings reveal that our proposed absolute binding affinity FEP method is appropriate for predicting HLA binding for disparate antigens with different genotypes. We also discuss atomic-level details of HLA genotypes interacting with gluten peptides and TCRs in regard to the pathogenesis of CeD.