The common use of plastics in daily life has engendered gigantic amounts of waste plastics, which have a detrimental influence on the environment. Researchers have proposed several strategies for the recycling of waste plastics and their products. Among these, one strategy is to use them in the construction industry, particularly in asphaltic pavements. This study thus focused on the utilization of waste plastics, specifically Low-Density Polyethylene (LDPE) and High-Density Polyethylene (HDPE), as an additive in Asphalt Concrete (AC) mixes. Indirect Tensile Strength (ITS), Flow Time (FT), and Dynamic Modulus (DM) tests were used to investigate the moisture damage, permanent deformation, fatigue performance, and DM of the LDPE and HDPE modified AC mixes. According to the laboratory test results, the LDPE and HDPE modified AC mixes offer more resistance to moisture damage compared to the Control AC mixes. It was also concluded that asphalt mixes modified with the LDPE and HDPE attained 2.07 times and 1.26 times superior resistance to permanent deformation than the Control mixes. Furthermore, the LDPE and HDPE modified AC mixes outperformed the DM values of the Control mixes by 2.06 times and 1.41 times, respectively. In addition, it was determined that the LDPE and HDPE modified AC mixes exhibit 1.72 times and 1.39 times greater fatigue parameter values than their counterpart, suggesting superior fatigue resistance performance. The statistical models developed using Response Surface Methodology (RSM) revealed the highest values of the Coefficient of Determination (>0.80), adequate precision (>4.0), and lack-of-fit tests, indicating the model’s adequacy for predicting the response.