Chemical investigation of the endophytic fungus Aspergillus sp. 16-5B cultured on Czapek’s medium led to the isolation of four new metabolites, aspergifuranone (1), isocoumarin derivatives (±) 2 and (±) 3, and (R)-3-demethylpurpurester A (4), together with the known purpurester B (5) and pestaphthalides A (6). Their structures were determined by analysis of 1D and 2D NMR spectroscopic data. The absolute configuration of Compound 1 was determined by comparison of the experimental and calculated electronic circular dichroism (ECD) spectra, and that of Compound 4 was revealed by comparing its optical rotation data and CD with those of the literature. The structure of Compound 6 was further confirmed by single-crystal X-ray diffraction experiment using CuKα radiation. All isolated compounds were evaluated for their α-glucosidase inhibitory activities, and Compound 1 showed significant inhibitory activity with IC50 value of 9.05 ± 0.60 μM. Kinetic analysis showed that Compound 1 was a noncompetitive inhibitor of α-glucosidase. Compounds 2 and 6 exhibited moderate inhibitory activities.