The paper investigates the improvement of bitumen mixture fatigue resistance and the rutting performance by using a specific low percentage of a styrene–butadiene–styrene (SBS) polymer, which contains polystyrene and polybutadiene compounds. A Fourier transform infrared (IR-FT) spectroscopy of the SBS polymer used in following test was carried out to ascertain the polybutadiene and polystyrene compound ratio, which may affect the modificant properties. Unmodified, low-percentage modified SBS, and common polymer-modified bitumen (PMB) as a reference were tested to ascertain the properties, fatigue resistance, and the rutting performance. The test results of the low-percentage modification with SBS are compared against unmodified mixtures and standard PMB mixtures. Finally, a simulation of the practical application was performed using the HDM-4 software (version 2.0), where the material research findings, with an emphasis on the rutting performance, were translated into the pavement performance with a varying binder course layer under simulated traffic conditions. Lifecycle analysis, with a focus on emissions production (CO2, SO2, and NOx) during pavement operation, was conducted for pavements with unmodified, low-percentage modified SBS, and standard PMB binder courses. The lifecycle analysis showed that a 3% modification of the binder course with the SBS polymer can extend the rutting parameter pavement lifecycle by approximately 34.5%, which is about half of the extension provided by the standard PMB modification. The resulting improvement in the pavement serviceability translated to a 9% reduction in CO2 and SO2 emissions and a 7.2% reduction in NOx emissions over a 20-year period.