To investigate the reflective crack-propagation behavior and provide control techniques for asphalt pavements widening, the finite-element models were built to simulate the widened asphalt pavement with a latent joint. The developed finite-element model considered the influence factors, including the loading modes (i.e., the symmetrical and unsymmetrical loading modes), the thickness and modulus of the asphalt concrete surface, the modulus of the new and existing stabilized bases, and the sheet stiffness of the reinforced geosynthetic. The finite-element simulation results show that increasing the thickness or reducing the modulus of the asphalt concrete surface effectively delays the propagation speed of the reflective cracks. The cracking potential reaches the minimum when the new and existing bases have a uniform modulus. Additionally, geosynthetic reinforcement across the joints significantly reduces the stress concentration around the crack tip and slows down the propagation of the reflective cracks. These benefits become greater when increasing the sheet stiffness of the geosynthetic. Finally, an experimental study was conducted to investigate the influence of the types of the asphalt overlay and the geosynthetic reinforcement on the reflective crack-propagation behavior. The experimental results indicate that the geosynthetic-reinforced structure with a lower modulus of the asphalt concrete surface significantly increases the fatigue life of widened pavements, and the polypropylene geotextile performs better than the glass-fiber grid in terms of the extension of the fatigue life.