Runner bean (Phaseolus coccineus L.) is a crop of significant economic importance in Mexico, but its inclusion in diets remains limited to certain regions. The bioprocessing of legumes through germination expands their consumption possibilities. Applying oxidative stress during germination has been suggested to improve the functional qualities of legume seeds. In this study, response surface methodology (RSM) with a central composite rotatable design (13 treatments) was used to identify the optimal hydrogen peroxide soaking concentration ([H₂O₂]; 0–35 mM) and germination time (Gt; 0–96 h) to enhance germination percentage (GP), free phenolic content (FPC), free flavonoid content (FFC), and antioxidant capacity in black runner bean sprouts. Regression analysis generated predictive models for each response. Optimal conditions were identified as [H₂O₂] of 30 mM and Gt of 92 h, achieving a GP of 95.7%. Under these conditions, sprouts exhibited increases FPC from 67.6 to 72.7 mg GAE/100 g dry weight (DW), FFC from 26.4 to 28.6 mg CE/100 g DW, ABTS^•+ scavenging activity from 3,028 to 3,782 mg TE/100 g DW, and oxygen radical absorbance capacity (ORAC) from 5,793 to 6,573 mg TE/100 g DW compared to those germinated without H₂O₂ stress. Soaking with 30 mM H₂O₂ enhanced the content of ferulic and p-coumaric acids in free and bound phenolic fractions, whereas catechin and quercetin showed notable reductions in both fraction as a result of H₂O₂ treatment. These findings reveal that H₂O₂ treatment can modify the phenolic profile of runner bean sprouts, thereby boosting their nutraceutical value.