When three welding conditions, including welding configuration, welding speed and laser power, are sequentially altered, supersaturation of liquid aluminum is crystallography-dependently determined to limit growth kinetics of dendrite tip with decease of thermo-metallurgical factors for solidification cracking to salvage the weld properties during emerging laser welding repair of multicomponent nickel-based single-crystal superalloy. After comparing growth crystallography between right side and left side of weld, the distribution of supersaturation of liquid aluminum is axis- symmetrically developed by favorite (001)/[100] dendrite growth kinetics, while the distribution is nonaxisymmetrically developed by detrimental (001)/[110] dendrite growth kinetics. High heat input is inappropriately procured by either high laser power or slow welding speed to insidiously boost supersaturation of liquid aluminum, worsen alloying partition and solute copiousness, heterogeneously exacerbate morphology and size of dendrite growth, whereby stray grain formation is strongly produced. In order to ameliorate dendrite growth, low heat input is usefully rendered by either low laser power or high welding speed to attenuate supersaturation of liquid aluminum, narrow solidification temperature range and obviate dendrite tip undercooling alongside columnar interface in order to augment crack-resistant dendrite of epitaxial growth. The overall supersaturation of liquid aluminum is crystallography-dependent. During across whole melt-pool solidification interface, supersaturation of nonsymmetric (001)/[110] welding configuration is not as small as symmetric (001)/[100] welding configuration under well-controlled heat input, thereby fosters the kinetic factors for stray grain development to obstruct columnar dendrite and consequently weaken unidirectional morphology. It is crystallographically favorable for relief of supersaturation with axis- symmetrical dendrite growth. The mechanism of crack-vulnerable dendrite growth elimination through circumspect improvement of supersaturation-controlled growth kinetics is constructively proposed for feasible crackless rejuvenation of laser welding or laser cladding. The theoretical predictions are scrupulously supported by corroborative metallograph observation.