A method of laser welding a workpiece stack-up that includes at least two overlapping metal workpieces is disclosed. The method includes advancing a beam spot of a laser beam relative to a top surface of the workpiece stack-up and along a beam travel pattern to form a laser weld joint, which is comprised of resolodified composite metal workpiece material, that fusion welds the metal workpieces together. And, while the beam spot is being advanced along the beam travel pattern, between a first point and a second point, which may or may not encompass the entire beam travel pattern, at least one of the following laser beam parameters is repeatedly varied: (1) the power level of the laser beam; (2) the travel speed of the laser beam; or (3) the focal position of the laser beam relative to the top surface of the workpiece stack-up.