A method of laser welding a workpiece stack-up (10) of overlapping steel workpieces (12, 14) involves heat-treating a region (64) of the stack-up (10) followed by forming a laser weld joint (66) that is located at least partially within the heat-treated region (64). During heat-treating, one or more pre-welding laser beams (68) are sequentially directed at a top surface (20) of the workpiece stack-up (10) and advanced along a pre-welding beam travel pattern (70) so as to reduce an amount of vaporizable zinc within the stack-up (10). Thereafter, the laser weld joint (66) is formed by directing a welding laser beam (82) at the top surface (20) of the workpiece stack-up (10) and advancing the welding laser beam (82) along a welding beam travel pattern (84) that at least partially overlaps with a coverage area of a pre-welding beam travel pattern (70) or a shared coverage area portion of multiple pre-welding beam travel patterns (70). The method can help reduce an amount of vaporizable zinc within the stack-up (10).