A new class of pyrimidine-based heterocycles has been successfully synthesized via a simple and efficient way starting from 2-keto-thiophene (1). The α,β-unsaturated ketone (chalcone) (3) was first synthesized by treating the ketone (1) with 4-methoxy benzaldehyde (2), followed by treating with amino formamidine hydrochloride to afford the intermediate pyrimidine moiety (4) which was converted to amide functionalized pyrimidines (5a–e), pyrimidine-2-imines (6a–e) and thiophene tethered pyrimidine-imidazoles (7a–e). The structures assigned to the new compounds are confirmed by IR, NMR, and MS studies. The newly synthesized compounds were subjected to a molecular docking study with the protein of Staphylococcus aureus (PDB ID: 1JIJ), for antioxidant and antibacterial activity. The compounds 5a, 6a, 6b, and 7d were found to show hydrogen bond interaction with active site amino acid residues with the binding energy of −8,08, −8.39, −8.64, and −8.02 kJ/mol, respectively, and may act as potential inhibitors of bacterial tyrosyl-tRNA synthetases. The biological study envisioned that the synthesized compound 7b has shown potent antioxidant properties with 74.07% scavenging activity at 400 µg/mL and compound 6b was found to exhibit excellent antibacterial activity with 16, 20, 21, and 22 mm zone of inhibition against S. aureus, Escherichia coli, Salmonella paratyphi-A and Bacillus subtilis bacterial strains, respectively.