A hydraulic fan circuit is disclosed. The hydraulic fan circuit may have a primary pump, a high-pressure passage fluidly connected to the primary pump, and a low-pressure passage fluidly connected to the primary pump. The hydraulic fan circuit may also have at least one accumulator in selective fluid communication with at least one of the high- and low-pressure passages, a motor, and a fan connected to the motor. The hydraulic fan circuit may further have a fan isolation valve fluidly connected to the high- and low-pressure passages. The fan isolation valve may be movable between a flow-passing position at which the motor is fluidly connected to the primary pump via the high- and low-pressure passages, and a flow-blocking position at which the motor is substantially isolated from the primary pump.