The antitumor drug 3-amino-1,2,4-benzotriazine-1,4-dioxide (tirapazamine, TPZ (1)) along with a number of newly synthesized tirapazamine derivatives (TPZs) bearing substitutions at the 3-amine position of TPZ (1) were estimated for their antibacterial activity against representative Gram-negative Escherichia coli (ATCC 25922) and Salmonella enterica (SL 5676), as well as Gram-positive Staphylococcus aureus (ATCC 25923) bacterial strains. Their activities in terms of minimum inhibitory concentrations (MICs) varied in the range of 1.1 µM (0.25 µg/mL)–413 µM (128 µg/mL). Amongst the most potent derivatives (1–6), acetyl- and methoxycarbonyl-substituted TPZs (2 and 4) were the strongest agents, which exhibited approximately 4–30 fold greater activities compared to those of TPZ (1) along with the reference drugs chloramphenicol (CAM) and nitrofurantoin (NFT). The inhibitory activities of the compounds were highly impacted by their structural features. No reliable relationships were established between activities and the electron-accepting potencies of the whole set of studied compounds, while the activities of TPZ drug (1) and the structurally uniform set of molecules (2–6) were found to increase with an increase in their electron-accepting potencies obtained by means of density functional theory (DFT) computation. A greater steric, lipophilic and polar nature of the substituents led to a lower activity of the compounds. The combined antibacterial in vitro trial gave clear evidence that TPZs coupled with the commonly utilized antibiotics ciprofloxacin (Cipro) and nitrofurantoin (NFT) could generate enhanced (suggestive of partial and virtually complete synergistic) and additive effects. The strongest effects were defined for TPZs–NFT combinations, which resulted in a notable reduction in the MICs of di-N-oxides. These preliminary findings suggest that the synthesized novel di-N-oxides might be used as sole agents or applied as antibiotic complements.