The electric turbocharger (ET) is a promising solution for engine downsizing. It provides great potential for vehicle fuel efficiency improvement. The ET makes engines run as hybrid systems so critical challenges are raised in energy management and control. This paper proposes a real-time energy management strategy based on updating and tracking of the optimal exhaust pressure setpoint. Starting from the engine characterization, the impacts of the ET on engine response and exhaust emissions are analyzed. A multivariable explicit model predictive controller is designed to regulate the key variables in the engine air system, whereas the optimal setpoints of those variables are generated by a high-level controller. The two-level controller works in a highly efficient way to fulfill the optimal energy management. This strategy has been validated in physical simulations and experimental testing. Excellent tracking performance and sustainable energy management demonstrate the effectiveness of the proposed method.