Diverse naphtho[1,2-b]furan-3-carboxamide derivatives 12a-12q were synthesized in high yield via the novel Re2O7-catalyzed formal [3 + 2] cycloaddition of 1,4-naphthoquinones with β-ketoamides as the key step. This methodology offers several advantages, such as environmentally benign character, the use of a mild catalyst, high yields, and ease of handling. The synthesized compounds were screened for their tyrosinase inhibitory, antioxidant, and antibacterial activities. The results showed that compound 12c exhibited excellent tyrosinase inhibitory activity with an IC50 of 13.48 μg/mL, which is comparable to that of kojic acid (IC50 = 19.45 μg/mL). Compounds 12a, 12b, and 12i displayed moderate antioxidant activities in a DPPH assay. Compound 12m showed good activity against S. aureus (MIC = 16 μg/mL), and compound 12p was found to be active against E. coli (MIC = 16 μg/mL).