In the years to come, Connected and Automated Vehicles (CAVs) are expected to substantially improve the road safety and environmental impact of the road transport sector. The information from the sensors installed on the vehicle has to be properly integrated with data shared by the road infrastructure (smart road) to realize vehicle control, which preserves traffic safety and fuel/energy efficiency. In this context, the present work proposes a real-time implementation of a control strategy able to handle simultaneously motion and hybrid powertrain controls. This strategy features a cascade of two modules, which were implemented through the model-based design approach in MATLAB/Simulink. The first module is a Model Predictive Control (MPC) suitable for any Hybrid Electric Vehicle (HEV) architecture, acting as a high-level controller featuring an intermediate layer between the vehicle powertrain and the smart road. The MPC handles both the lateral and longitudinal vehicle dynamics, acting on the wheel torque and steering angle at the wheels. It is based on a simplified, but complete ego-vehicle model, embedding multiple functionalities such as an adaptive cruise control, lane keeping system, and emergency electronic brake. The second module is a low-level Energy Management Strategy (EMS) of the powertrain realized by a novel and computationally light approach, which is based on the alternative vehicle driving by either a thermal engine or electric unit, named the Efficient Thermal Electric Skipping Strategy (ETESS). The MPC provides the ETESS with a torque request handled by the EMS module, aiming at minimizing the fuel consumption. The MPC and ETESS ran on the same Microcontroller Unit (MCU), and the methodology was verified and validated by processor-in-the-loop tests on the ST Microelectronics board NUCLEO-H743ZI2, simulating on a PC-host the smart road environment and a car-following scenario. From these tests, the ETESS resulted in being 15-times faster than than the well-assessed Equivalent Consumption Minimization Strategy (ECMS). Furthermore, the execution time of both the ETESS and MPC was lower than the typical CAN cycle time for the torque request and steering angle (10 ms). Thus, the obtained result can pave the way to the implementation of additional real-time control strategies, including decision-making and motion-planning modules (such as path-planning algorithms and eco-driving strategies).