Bitumen shows visco-elastic behavior, exhibiting both elastic and viscous properties as predicted by dynamic response and phase angle. Modern asphalt bituminous pavements face issues such as early-stage fatigue cracks, rutting, and permanent deformations due to low-temperature cracking, high-temperature deformation, moisture susceptibility, and overloading. These pavement distresses result in the formation of potholes, alligator cracks, and various deformations, which accelerate the need for rehabilitation and maintenance. To address these concerns, this study focused on utilizing Nitrile Butadiene Rubber derived from surgical gloves as an additive in conventional asphalt pavements to assess its effect on stiffness. Nitrile Butadiene Rubber was added in intervals of 2%, 4%, 6%, and 8% to conventional bituminous pavement. The rheological properties, marshall properties, dynamic modulus, and phase angle were evaluated for varying percentages of Nitrile Butadiene Rubber at different temperature, and frequency. The dynamic response was determined using a simple performance tester at four different temperatures (4.4°C, 21.1°C, 37.8°C, and 54.4°C) and six different frequencies (0.1, 0.5, 1, 5, 10, and 25Hz). Response surface methodology was employed to establish a relationship between input and output variables and to optimize the amount of Nitrile Butadiene Rubber in the mix based on dynamic modulus and phase angle. The study concluded that adding up to 6% of Nitrile Butadiene Rubber improved Marshall stability, while higher percentages led to reduced stability. A similar trend was observed in the dynamic modulus, which peaked with the addition of 6% Nitrile Butadiene Rubber, regardless of frequency and temperature. The response surface methodology model indicated that coupling the percentage of Nitrile Butadiene Rubber with frequency increased the dynamic modulus at a constant temperature, with the highest value occurring at 4.4°C. However, the dynamic modulus decreased as the temperature rose for the same combinations of Nitrile Butadiene Rubber percentages and frequencies. Numerical optimization suggested that a maximum of 5.9% Nitrile Butadiene Rubber should be added to achieve the highest dynamic modulus and lowest phase angle.