A fuel supply system for a gas burner assembly is provided. The gas burner assembly includes an inner burner stage positioned concentrically within an outer burner stage. The fuel supply system includes a fuel supply for providing a primary flow of fuel through a primary fuel conduit and a single outlet control valve operably coupled to the primary fuel conduit. A first and second fuel supply conduit split off of the primary fuel conduit and are fluidly coupled with the outer burner stage and the inner burner stage, respectively. A shutoff valve is operably coupled to one of the first fuel supply conduit and the second fuel supply conduit and is configured for closing when a flow rate of fuel through the shutoff valve drops below a predetermined flow rate.