A method of resistance spot brazing a workpiece stack-up that includes a first thin-gauge steel workpiece and a second thin-gauge steel workpiece. The method includes several steps. A first step involves applying a filler material to a surface of the first thin-gauge steel workpiece. A second step involves bringing a surface of the second thin-gauge steel workpiece to adjoin the filler material. A third step involves clamping a first welding electrode and a second welding electrode on the first and second thin-gauge steel workpieces and over the filler material. A fourth step involves passing electrical current between the first and second welding electrodes and hence through the filler material. And a fifth step involves terminating passage of the electrical current in order to establish a brazed joint between the first and second thin-gauge steel workpieces.