Background/Objectives: Antimicrobial resistance (AMR) presents a medical risk as well as a significant global socioeconomic challenge. Key contributors to AMR include the excessive use and incorrect application of antibiotics in humans and agriculture, nosocomial infections, and the absence of new classes of antibiotics. Methods: Novel dibrominated tricyclic flavonoids have been synthesized from the corresponding 3-dithiocarbamic flavanones and their antimicrobial and cytotoxicity properties have been investigated. Results: It has been found that these tricyclic flavonoids exhibit strong antimicrobial properties against clinically relevant pathogens such as Staphylococcus aureus, Acinetobacter baumannii, and Escherichia coli with MIC and MBC values against S. aureus ATCC 25923 as low as 0.12 µg/mL and 1.9 µg/mL, respectively. Conclusions: The synthetic tricyclic flavonoids exhibit strong antibacterial activity against selected WHO priority pathogens, including Staphylococcus aureus and Acinetobacter baumannii, surpassing the efficacy of both natural and synthetic flavonoids and several conventional antibiotics.