A regulator valve regulates pressure of transmission fluid applied to a clutch of a transmission and a flow rate of the transmission fluid from the regulator valve to a transmission fluid sump. A transmission fluid pump is driven by an engine of the vehicle. A control module, while an ignition system of the vehicle is ON, selectively shuts down the engine of the vehicle for an auto-stop event. A target pressure module, before an engine speed reaches zero for the auto-stop event, increases a target value of a pressure of the transmission fluid at an output of the transmission fluid pump. A regulator control module, before the engine speed reaches zero for the auto-stop event and based on the increase in the target value of the pressure, adjusts the regulator valve to increase the pressure of the transmission fluid at the output of the transmission fluid pump.