A series of nine thiazole–hydrazone hybrids (D1–D9) was prepared in two steps: 5-chloro-1,3-dimethyl-1H-pyrazole-4-carbaldehyde was condensed with thiosemicarbazide, and the resulting thiosemicarbazone was cyclized with substituted phenacyl bromides. The products were characterized by Fourier-transform infrared (FT-IR) spectroscopy, 1H and 13C nuclear magnetic resonance (NMR) spectroscopy and mass spectrometry. Antibacterial activity against Staphylococcus aureus, Bacillus subtilis, Escherichia coli and Klebsiella pneumoniae, and antifungal activity against Candida albicans, were screened by the Kirby–Bauer disc diffusion method. Compounds D1, D2 and D7 were the most promising, mainly against the Gram-negative strains and C. albicans. Docking of the most active compounds into four microbial target proteins (Protein Data Bank IDs 4URM, 1KZN, 5ECX and 5TZ1) gave binding energies of −6.7 to −8.7 kcal/mol, with hydrogen-bonding and hydrophobic contacts in the active sites. Density functional theory (DFT) calculations supplied frontier orbital energies, reactivity descriptors and electrostatic potential maps, and in silico absorption, distribution, metabolism and excretion (ADME) screening suggested drug-like behavior. These results point to thiazole–hydrazone hybrids as useful starting points for antimicrobial lead development.