A cooling system and method are provided for facilitating cooling of a liquid-cooled electronics rack. The cooling system includes a coolant flow controller, a modular cooling unit and a pressure controller. The flow controller is associated with a respective electronics rack and controls flow of coolant through that electronics rack based on its changing cooling requirements. The cooling unit includes an adjustable coolant pump for facilitating supply of coolant to the rack. The pressure controller is associated with the cooling unit for controlling pressure of coolant at an output of the cooling unit via control of pump speed of the pump. Responsive to adjusting coolant flow through the electronics rack, the pressure controller automatically adjusts pump speed of the adjustable pump to maintain pressure about a constant coolant pressure set point at an output of the cooling unit, thereby conserving power while still cooling the liquid-cooled electronics rack.