Green synthesis of metal nanoparticles using plant sources is one of the most environmentally sound, economically safer, and operationally simple approaches compared with their physiochemical methods. In this work, we have developed the biogenic synthesis of Ag nanoparticles using the aqueous peel extract of Punica granatum L. fruit, which mitigates the requirement for any hazardous reagents or toxic chemicals. The ultraviolet-visible spectrum confirmed the formation of Ag@PPE NPs with an absorption peak at 420 nm. The X-ray diffraction analysis confirms that the biosynthesized Ag@PPE NPs are crystalline, with a crystallite size of 9.23 nm. SEM and TEM images revealed the spherical morphology of Ag@PPE NPs, with particle sizes ranging from 2 to 20 nm. The biosynthesized Ag@PPE NPs were explored as antimicrobial agents against both Gram-positive (CA-MRSA) and Gram-negative (Escherichia coli) bacteria as well as Candida albicans (ATCC 14053). The mean zone of inhibition against the CA-MRSA group was 15.34 ± 2.5 mm, while it was 12.33 ± 1.5 mm against E. coli. In this study, Ag@PPE NPs demonstrated strong antibiofilm activity and antioxidant activity. Moreover, the catalytic applicability of the synthesized Ag@PPE NPs has been investigated for the oxidative hydroxylation of differently substituted aryl boronic acids into phenols at room temperature. The reaction proceeded efficiently in a short reaction time, and the desired products were obtained with high to excellent yields (82%–94%). Notably, the nanocatalyst can be recovered in five consecutive runs without decreasing its catalytic performance. The plausible mechanism of this ipso-hydroxylation reaction is well presented.