The flash-tank-cycle vapor injection technique has been developed for heat pump operation under cold climate, however, lack of effective control strategy has limited its practical acceptance. This paper presents a novel control strategy for a two-stage air source heat pump water heater with flank-tank-cycle vapor injection. The intermediate pressure setpoint for the injection loop is regulated by the upper electronic expansion valve. Then, a real-time optimization or optimal control framework adjusts the intermediate pressure setpoint to minimize the total power consumption, with the compressor capacity used to satisfy the load demand via an inner-loop controller. In particular, the extremum seeking controller is applied as a model-free real-time optimization strategy for such purpose. To evaluate the proposed control strategy, a Modelica based dynamic simulation model is developed for such system. Simulations under fixed, staircase and realistic ambient temperature profiles validate the effectiveness of the proposed control strategy. Besides real-time optimization of system efficiency, a major merit of this strategy is to retain the use of saturated vapor for the injection line, instead of levitating the superheat. The inherent efficiency of the flash tank cycle is thus maintained without additional devices, and the liquid level can be maintained in a proper range.