This study aimed to optimize the enzymatic process for extracting narirutin from yuzu pomace while maximizing yield, and to assess its functional properties related to prebiotic, antimicrobial, and anti-allergic activities. Given the high pectin content in yuzu pomace, which increases extract viscosity and impedes the release of bioactive compounds, a sequential enzyme treatment was implemented. Pectinase (P4) was first used to degrade pectin, followed by cellulase (C1) to facilitate the release of narirutin. The P4–C1 extract achieved a 2.17-fold increase in narirutin content compared to the crude extract without enzyme treatment. In prebiotic activity, the P4–C1 extract enhanced the growth of Lactobacillus plantarum and Bifidobacterium infantis by 34.62% and 28.03%, respectively, compared to the crude extract. Additionally, the P4–C1 extract demonstrated improved antimicrobial activity against Salmonella typhimurium, Staphylococcus epidermidis, and Staphylococcus aureus, with increases of 22.69%, 27.09%, and 25.04%, respectively. Furthermore, in anti-DNP-IgE-sensitized RBL-2H3 cells, the P4–C1 extract showed enhanced anti-allergic activity by reducing β-hexosaminidase release by 16.22% compared to the crude extract. These findings indicate that the optimized enzymatic process significantly improves narirutin extraction efficiency and that the extract has considerable potential as a functional ingredient for prebiotic, antimicrobial, and anti-allergic applications.