Four naphtho-γ-pyrones (fonsecinones A and C and aurasperones A and E) were identified as potential antibacterial agents against Escherichia coli, extended-spectrum β-lactamase (ESBL)-producing E. coli, Pseudomonas aeruginosa, Enterococcus faecalis, and methicillin-resistant Staphylococcus aureus (MRSA) in an in vitro antibacterial screen of 218 fungal metabolites. Fonsecinone A (2) exhibited the most potent antibacterial activity, with minimum inhibitory concentrations (MICs) of 4.26, 17.04, and 4.26 μg/mL against ESBL-producing E. coli, P. aeruginosa, and E. faecalis, respectively. The inhibitory effects of fonsecinones A (2) and C (3) against E. coli and ESBL-producing E. coli were comparable to those of amikacin. Molecular docking-based target identification of naphtho-γ-pyrones 1-8 revealed bacterial enoyl-acyl carrier protein reductase (FabI) as an antibacterial target, which was further validated by FabI affinity and inhibition assays. Fonsecinones A (2) and C (3) and aurasperones A (6) and E (7) bound FabI specifically and produced concentration-dependent inhibition effects. This work is the first report of anti-drug-resistant bacterial activities of naphtho-γ-pyrones 1-8 and their possible antibacterial mechanism of action and provides an example of the successful application of in silico methods for drug target identification and validation and the identification of new lead antibiotic compounds against drug-resistant pathogens.