Background/Objectives: Coronary artery disease (CAD) remains the leading global cause of mortality, underscoring the need for functional assessments that extend beyond anatomical evaluation. The Hyperemic Stenosis Resistance (HSR) index combines invasive pressure and flow parameters to assess stenosis severity but faces limitations due to methodological and standardization challenges. This study aimed to introduce and validate a novel non-invasive computational equivalent of HSR (cHSR), derived from coronary computed tomography angiography (CCTA), and to compare its diagnostic performance with fractional flow reserve derived from computational fluid dynamics (FFR_CFD) and quantitative flow ratio (QFR). Methods: A retrospective analysis was conducted on 64 patients (106 coronary lesions) with suspected chronic coronary syndrome (CCS) who underwent both CCTA and invasive coronary angiography (ICA). Computational simulations incorporated patient-specific boundary conditions based on CCTA-derived left ventricular and aortic flow data. Diagnostic accuracy for predicting revascularization was compared among cHSR, FFR_CFD, and QFR. Results: FFR_CFD showed a strong correlation with invasive FFR (r = 0.87, p < 0.0001). The cHSR index achieved the highest diagnostic accuracy (96.2%) at an optimal cut-off of 0.75 mmHg/cm·s⁻¹, outperforming both FFR_CFD and QFR. No significant correlation was found between cHSR and shear stress parameters, including the Oscillatory Shear Index (OSI) and Time-Averaged Wall Shear Stress (TAWSS), indicating complex hemodynamic interactions beyond simple flow–pressure relationships. Conclusions: The computational hyperemic stenosis resistance (cHSR) index represents a promising non-invasive tool for the functional assessment of CAD, demonstrating superior diagnostic performance compared with existing imaging-based indices. Prospective multicenter studies with larger populations are warranted to confirm its clinical applicability and prognostic value in chronic coronary syndrome management.