For the heating, ventilating, and air conditioning (HVAC) systems for commercial buildings, there has been a greater demand for reducing energy consumption. The economizers have been developed as a class of energy-saving HVAC devices that may increase the energy efficiency by taking advantage of outdoor air during cool or cold weather. However, many economizers do not operate in the expected manner and waste even more energy than before installation, mostly due to the unreliable sensors and actuators in practice. Better control strategy is needed for optimal and robust operation. In this paper, an extremum seeking control (ESC) based self-optimizing strategy is proposed to minimize the energy consumption, with the feedback of chilled water supply command rather than the temperature and humidity measurements. The mechanical cooling load is minimized by seeking the optimal outdoor-air damper opening in real time. Such scheme does not need temperature and humidity sensors and depends much less on the knowledge of economizer model. Simulation was performed on a Modelica based transient model of a single-duct air-handling unit (AHU) developed with Dymola and AirConditioning Library. The simulation results demonstrated the potential of using ESC to achieve the minimal mechanical cooling load in a self-optimizing manner. In addition, an anti-windup ESC scheme is proposed to handle the ESC windup due to actuator (damper) saturation. The simulation results validated the effectiveness of the proposed anti-windup ESC.