This study designed an efficient, easily implementable online optimal control strategy for three-power-source hybrid electric powertrains. The energy improvement of optimal energy management and integrated optimal energy management/mode switch timing relative to the energy consumption in rule-based control was evaluated. First, a control-oriented vehicle model with seven subsystems was developed. For achieving rule-based control, the torque distribution among the engine, motor, and generator was designed according to performance maps of power sources. To conduct power allocation of three sources, two power-split ratios were obtained. Furthermore, for switching between three operation modes (hybrid, electric vehicle, and range extension modes), two hysteresis zones based on the required power and battery state-of-charge were used with four designed variables (boundaries). A global search method was used for the optimization. A cost function with a physical-constraint penalty was used to maximize the travel distance. A simulation performed using nested-structure for-loop programs showed that the mileage extension (energy improvement) for the optimal energy management and integrated optimal energy management/mode switch timing relative to the mileage in rule-based control for two driving cycles, NEDC and FTP-75, were [26.32%, 30.52%] and [17.22%, 20.68%], respectively. The improvements of CO2 reduction were [26.34%, 27.10%] and [23.47%, 24.12%], respectively, thus proving that this study significantly reduced energy consumption and pollutant emission by employing an easily designed control strategy. Online parameter tuning and implementation of optimal energy management in a real vehicle will be conducted in the future.