A method of laser welding a workpiece stack-up that includes two or more overlapping metal workpieces is disclosed. The disclosed method includes directing a laser beam at a top surface of the workpiece stack-up to create a molten metal weld pool and, optionally, a keyhole, and further gyrating the laser beam to move a focal point of the laser beam along a helical path having a central helix axis oriented transverse to the top and bottom surfaces of the workpiece stack-up. The gyration of the laser beam may even be practiced to move the focal point of the laser beam along a plurality of helical paths so as to alternately convey the focal point back-and-forth in a first overall axial direction and a second overall axial direction while advancing the laser beam relative to the top surface of the workpiece stack-up along a beam travel pattern.