The present study evaluated the effects of ultraviolet B (UVB) radiation and wounding stress, applied alone or combined, on the biosynthesis of phenolic compounds and ascorbic acid in the peel and pulp of red prickly pear (Opuntia ficus-indica cv. Rojo Vigor). Whole and wounded-fruit samples were treated with UVB radiation (6.4 W·m−2) for 0 and 15 min, and stored for 24 h at 16 °C. Phytochemical analyses were performed separately in the peel and pulp. The highest phenolic accumulation occurred after storage of the whole tissue treated with UVB, where the main phenolic compounds accumulated in the peel and pulp were quercetin, sinapic acid, kaempferol, rosmarinic acid, and sinapoyl malate, showing increases of 709.8%, 570.2%, 442.8%, 439.9%, and 186.2%, respectively, as compared with the control before storage. Phenylalanine ammonia-lyase (PAL) activity was increased after storage of the whole and wounded tissue treated with UVB light, and this increase in PAL activity was associated to phenolic accumulation. On the other hand, l-galactono-γ-lactone dehydrogenase (GalLDH) activity and ascorbic acid biosynthesis was enhanced due to UVB radiation, and the effect was increased when UVB was applied in the wounded tissue showing 125.1% and 94.1% higher vitamin C content after storage when compared with the control. Respiration rate was increased due to wounding stress, whereas ethylene production was increased by wounding and UVB radiation in prickly pears. Results allowed the generation of a physiological model explaining the UVB and wound-induced accumulation of phenolic compounds and ascorbic acid in prickly pears, where wounding facilitates UVB to access the underlying tissue and enhances an apparent synergistic response.