Chemical epigenetic modification on a marine-derived fungus Aspergillus terreus RA2905 using a histone deacetylase inhibitor, suberoylanilide hydroxamic acid (SAHA), resulted in a significantly changed metabolic profile. A chemical investigation of its ethyl acetate (EtOAc) extract led to the isolation of a racemate of benzyl furanone racemate (±)-1, which further separated chirally as a pair of new enantiomers, (+)- and (−)-asperfuranone (1), together with two new benzyl pyrones, asperpyranones A (2) and B (3). Their structures were elucidated by analysis of the comprehensive spectroscopic data, including one-dimensional (1D) and two-dimensional (2D) NMR, and HRESIMS. The absolute configurations were determined by electronic circular dichroism (ECD) calculation and single-crystal X-ray crystallographic experiment. The structures with benzyl furanone or benzyl pyrone skeletons were discovered from natural products for the first time. Compounds (±)-1, (+)-1, (−)-1, and 2 displayed the antifungal activities against Candida albicans with MIC values of 32, 16, 64, and 64 μg/mL and PTP1B inhibitory activities with the IC50 values of 45.79, 17.32, 35.50, and 42.32 μM, respectively. Compound 2 exhibited antibacterial activity against Pseudomonas aeruginosa with the MIC value of 32 μg/mL.