Crumb rubber-modified asphalt concrete (CMAC) has gained increasing attention as a sustainable pavement material capable of improving mechanical performance while utilizing waste tire resources. This study investigates the rutting resistance and fatigue behavior of CMAC using a combined experimental and mechanistic–empirical modeling approach. Asphalt mixtures containing 0–25% crumb rubber by binder weight were prepared and evaluated through Marshall stability and indirect tensile fatigue tests, whereas Fourier-transform infrared spectroscopy (FTIR) was used to examine binder–rubber interactions. The results indicate that crumb rubber significantly influences both the volumetric and mechanical properties of asphalt mixtures. Mixtures containing 10–15% crumb rubber exhibited optimal performances, achieving up to 36% higher Marshall stability and improved fatigue life compared with conventional asphalt mixtures. FTIR analysis revealed that rubber particle swelling and limited chemical interactions enhanced binder elasticity and improved binder–aggregate compatibility. However, excessive rubber content (≥20%) resulted in reduced stability owing to increased binder absorption and decreased effective binder film thickness. A mechanistic–empirical model incorporating viscoelastic, viscoplastic, and fatigue damage parameters successfully reproduced the experimental trends and identified the same optimal rubber content range. The findings demonstrate that CMAC with a moderate rubber content can enhance pavement durability and structural performance while promoting environmentally sustainable road construction through the reuse of waste tires.