Phytochemical investigation applying GC (gas chromatography)-MS (mass spectrometry)/GC-FID (flame ionization detection) on the hydro-distilled essential oils of the Vietnamese medicinal plant Uvaria boniana leaf and twig lead to the detection of 35 constituents (97.36%) in the leaf oil and 52 constituents (98.75%) in the twig oil. Monoterpenes, monoterpenoids, sesquiterpenes, and sesquiterpenoids were characteristic of U. boniana essential oils. The leaf oil was represented by major components (E)-caryophyllene (16.90%), bicyclogermacrene (15.95%), α-humulene (14.96%), and linalool (12.40%), whereas four compounds α-cadinol (16.16%), epi-α-muurolol (10.19%), α-pinene (11.01%), and β-pinene (8.08%) were the main ones in the twig oil. As compared with the leaf oil, the twig oil was better in antimicrobial activity. With the same MIC value of 40 mg/mL, the twig oil successfully controlled the growth of Gram (+) bacterium Bacillus subtilis, Gram (−) bacterium Escherichia coli, fungus Aspergillus niger, and yeast Saccharomyces cerevisiae. In addition, both two oil samples have induced antiinflammatory activity with the IC50 values of 223.7–240.6 mg/mL in NO productive inhibition when BV2 cells had been stimulated by LPS. Docking simulations of four major compounds of U. boniana twig oil on eight relevant antibacterial targets revealed that epi-α-muurolol and α-cadinol are moderate inhibitors of E. coli DNA gyrase subunit B, penicillin binding protein 2X and penicillin binding protein 3 of Pseudomonas aeruginosa with similar free binding energies of −30.1, −29.3, and −29.3 kJ/mol, respectively. Furthermore, in silico ADMET studies indicated that all four docked compounds have acceptable oral absorption, low metabolism, and appropriated toxicological profile to be considered further as drug candidates.