The integrated path tracking control (PTC) of steering and braking is crucial for enhancing the stability of autonomous vehicles under extreme conditions. In the present study, a control input dimensionality-reducing method and an asynchronous sampling method are presented to address the problem of the high computational cost of the steering and braking integrated path tracking controller (PTCer) based on model predictive control (MPC). First, based on tire friction limit and tire force utilization, the control input dimensionality-reducing method is designed and a vehicle model with reduced dimensionality of control input is derived. Second, the rolling iteration mechanism of MPC is analyzed and a variable-scale asynchronous sampling method between the control loop and prediction horizon is designed with the control horizon as the boundary. Finally, the integrated MPC-PTCer based on control input dimensionality-reducing and asynchronous sampling is designed. The real-time performance (RTP), path tracking accuracy, and vehicle stability of the proposed integrated MPC-PTC are tested and evaluated through the simulation and the hardware-in-the-loop platform. The test results of different test conditions show that the proposed integrated MPC-PTC improves the RTP by more than 70% and ensures the path tracking accuracy and lateral stability of autonomous vehicles under extreme conditions.