The performance and durability of asphalt pavements are strongly influenced by the rheological properties of asphalt binders, particularly under severe climatic and traffic conditions. This study investigates the synergistic effects of incorporating multi-walled carbon nanotubes (CNTs) at dosages ranging from 0.25% to 1% into AC 40-50 asphalt binders modified with 4% Styrene–Butadiene–Styrene (SBS). A comprehensive experimental program involving physical, rheological, and chemical characterization tests was conducted, including penetration, softening point, viscosity, storage stability, a Dynamic Shear Rheometer (DSR), Multiple Stress Creep Recovery (MSCR), Linear Amplitude Sweep (LAS), Fourier Transform Infrared Spectroscopy (FTIR), and Glover–Rowe (G-R) analysis. Statistical inference using one-way ANOVA was also conducted to evaluate the significance of differences among the binder formulations investigated. The results showed a continuous increase in binder stiffness with increasing CNT content, as indicated by decreasing penetration values, higher softening points, and increased viscosity. Incorporating 1% CNT reduced the softening-point difference from 3.1 °C to 1.6 °C in SBS-modified binders, indicating improved storage stability. Rheological evaluations showed that 0.75% CNT increased the high-temperature performance grade from 82 °C to 88 °C and provided the best rutting resistance, as indicated by MSCR results. In contrast, the 0.5% CNT formulation exhibited superior fatigue resistance and the lowest Glover–Rowe index, indicating improved cracking resistance and durability. Overall, the findings demonstrate that CNTs can effectively enhance the performance of SBS-modified asphalt binders, with 0.75% CNT being optimal for hot-climate applications, while 0.5% CNT exhibited improved fatigue and cracking resistance under moderate-temperature conditions.