A thiazole-based hydrazone derivative, (E)-2-(2-(1-(5-chlorothiophen-2-yl)ethylidene)hydrazinyl)-4-(naphthalen-2-yl)thiazole, was successfully synthesized via a convenient one-pot multicomponent reaction using 1-(5-chlorothiophen-2-yl)ethan-1-one, thiosemicarbazide, and 2-bromo-1-(naphthalen-2-yl)ethan-1-one. The structure of the synthesized compound was confirmed by FT-IR, 1H NMR, and 13C NMR spectroscopy. Density Functional Theory (DFT) calculations at the B3LYP/6-311G(d, p) level were performed to investigate the optimized molecular geometry, frontier molecular orbitals, and global reactivity descriptors. The calculated HOMO and LUMO energies were −5.56 and −1.59 eV, respectively, with an energy gap of 3.97 eV, indicating moderate chemical reactivity and good kinetic stability. Antimicrobial studies demonstrated moderate antibacterial activity against Escherichia coli (14 mm), Pseudomonas aeruginosa (14 mm), and Staphylococcus aureus (19 mm), while weak antifungal activity was observed against Candida albicans (7 mm). Molecular docking against Escherichia coli DNA gyrase B (PDB ID: 6YD9) revealed a strong binding affinity (−9.2 kcal mol⁻¹), stabilized through π-anion, π-sigma, and π-alkyl interactions with key active-site residues, including Asp49, Ile78, Val43, Ala47, Val120, and Val167. SwissADME analysis predicted favorable drug-likeness with Lipinski compliance, no blood–brain barrier permeability, no P-glycoprotein substrate liability, and low cytochrome P450 inhibition, although poor aqueous solubility and low gastrointestinal absorption were predicted. This integrated experimental and computational results identify this thiazole hydrazone as a promising scaffold for the development of new antibacterial agents.