A fluid pressure regulator includes a regulator housing having an inlet end and an outlet end; a flexible flow tube extending between the inlet end and the outlet end; a hollow piston located at a downstream location relative to a mid-portion of the flow tube in a direction of flow of fluid through the regulator housing; a first chamber above the piston and a second chamber below the piston; a passage establishing fluid communication between the outlet end and the first chamber; and at least one pinch arm pivotally mounted at one end within the regulator housing and movable in response to movement of the piston by an increase in fluid pressure in the first chamber so that an opposite end of the at least one pinch arm will pinch a portion of the flow tube and thereby restrict flow through the flow tube.