A method of laser welding a workpiece stack-up (10) that includes at least two overlapping steel workpieces (12, 14) comprises directing a laser beam (40) at a top surface (26) of the workpiece stack-up to form a keyhole (56) surrounded by a molten steel weld pool (58). The laser beam is conveyed along a predefined weld pattern that includes one or more nonlinear inner weld paths (66) and an enclosed outer peripheral weld path (68) surrounding the one or more nonlinear inner weld paths. During conveyance of the laser beam along the one or more nonlinear inner weld paths, the keyhole fully penetrates through the workpiece stack-up from the top surface of the stack-up to the bottom surface (28) of the stack-up. The method produces weld joints between the steel workpieces that do not have an intentionally imposed gap formed between their faying surfaces.