An agricultural sprayer includes a purge tank, a nozzle configured to dispense an agricultural fluid onto an underlying field, and a downstream valve configured to selectively permit the air from the main fluid conduit to flow to the nozzle. A computing system is configured to initiate a purging operation to purge the agricultural fluid present within the nozzle and, upon receipt of the input, control an operation of a main valve such that the main valve is moved to an opened position to allow the air to flow through a main fluid conduit. In addition, the computing system is configured to monitor a first air pressure associated with the purge tank and a second air pressure associated with the nozzle. Furthermore, the computing system is configured to control an operation of the downstream valve during the purging operation based on the monitored first and second air pressures.