A rational optimization for the synthesis of galacto-oligosaccharides (GOS) from lactose catalyzed by β-galactosidase from Aspergillus aculeatus, included in the commercial product Pectinex Ultra SP-L, has been performed by using experimental design and surface response methodology. This accurate tool optimized empirical production of the most desired high-GOS (tri-GOS and tetra-GOS) up to 16.4% under the following reaction conditions: 59 °C, 4 U/mL free enzyme concentration, pH 6.5, 250 g/L initial lactose concentration, and 20 h of reaction. The statistical analysis revealed temperature and initial lactose concentration as critical parameters. The successful immobilization of the enzyme on a glyoxyl-functionalized porous silica support slightly increased the yield toward high-GOS (17.6%), especially tri-GOS yield (15.3%), under the optimized reaction conditions as compared to the free enzyme. Furthermore, the promotion of the transgalactosylation reaction toward tri-GOS production increased 1.5-fold the productivity of high-GOS as compared to the free enzyme.