A hydraulic control system is disclosed. The hydraulic control system may have an input device to generate a first signal indicative of a desired swing motor movement, and a control valve configured to selectively pass fluid to the swing motor and drain from the swing motor to drive the swing motor based on the first signal. The hydraulic control system may also have a pressure sensor to generate a second signal indicative of a swing motor pressure, a speed sensor configured to a third signal indicative of a swing motor speed, and a controller configured to make a comparison of at least one of the swing motor speed and the swing motor pressure with a threshold speed and a threshold pressure, and open the control valve to drain fluid from the swing motor to the tank based on the comparison when the input device is in a neutral condition.