The development and spread of resistance of human pathogenic bacteria to the action of commonly used antibacterial drugs is one of the key problems in modern medicine. One of the especially dangerous and easily developing antibiotic resistant bacterial species is Staphylococcus aureus. Anthra[1,2-d][1,2,3]triazine-4,7,12(3H)-triones 22–38 have been developed as novel effective antistaphylococcal agents. These compounds have been obtained by sequential conversion of 1-amino-9,10-dioxo-9,10-dihydroanthracene-2-carboxylic acid (1) and 1-amino-4-bromo-9,10-dioxo-9,10-dihydroanthracene-2-carboxylic acid (2) into the corresponding amides 5–21, followed by subsequent endo-cyclization under the influence of sodium nitrite in acetic acid. Evaluation of the antimicrobial activity of the synthesized compounds against selected species of Gram-positive and Gram-negative bacteria as well as pathogenic yeasts of the Candida genus has been carried out by the serial dilution method. It has been established that anthra[1,2-d][1,2,3]triazine-4,7,12(3H)-triones exhibit selective antibacterial activity against Gram-positive bacteria. Eight, six and seven, out of seventeen compounds tested, effectively inhibited the growth of S. aureus ATCC 25923, S. aureus ATCC 29213 and S. epidermidis ATCC12228, respectively, at a concentration equal to 1 µg/mL or lower. The high antistaphylococcal potential of the most active compounds has been also confirmed against clinical isolates of S. aureus, including the MRSA strains. However, bacteria of the Staphylococcus genus have demonstrated apparent resistance to the novel compounds when grown as a biofilm. None of the four selected compounds 3234 and 36 at a concentration of 64 µg/mL (128 or 256 × MIC—against planktonic cells) has caused any decrease in the metabolic activity of the staphylococcal cells forming the biofilm. The kinetic time–kill assay revealed some important differences in the activity of these substances. Compound 33 is bacteriostatic, while the other three demonstrate bactericidal activity.