Background: Natural integrastatins and their synthetic derivatives with the oxocine ring exhibit a wide range of antiviral activities, including activities against HIV-1 and SARS-CoV-2 viruses, which makes these compounds interesting for pharmaceutical purposes. Objectives: A series of novel derivatives of 9-methyl-substituted epoxybenzo[7,8]oxocino[4,3-b]pyridine were synthesized, characterized and studied for antiviral activity using an in silico approach. Methodology: Synthesis was carried out based on 3,5-diacetyl-2,6-dimethylpyridine and S-methylthio- and N-methylamino derivatives of salicylic aldehyde. The structure of the newly synthesized compounds was confirmed by 1H and 13C NMR, chromato-mass spectrometry, and elemental analysis. Their physicochemical properties and antiviral potential were studied using DFT B3LYP/6–311++G(d,p) CPCM (water) calculations, molecular docking, and molecular dynamics simulations. Results: As a result of the study, optimal synthesis parameters (solvent, reaction time, amount and type of acid catalyst, temperature, etc.) were selected for each of the nine novel 9-methyl-substituted epoxybenzo[7,8]oxocino[4,3-b]pyridine derivatives, ensuring good yields. Using an in silico approach, antiviral activity towards viral proteins of human rhinovirus 14, HIV-1 integrase, SARS-CoV-2 RNA-dependent polymerase was predicted and evaluated for all derivatives. Compound 6i from the series of newly synthesized derivatives was selected as the best one because it demonstrated excellent binding affinity to HIV-1 protein and high stability of the protein-ligand complex. However, in silico evaluation of ADMET properties revealed that compound 6i was the least favorable candidate due to its limited absorption, high predicted toxicity, and poor metabolic stability. In contrast, compounds 6b, 6d, and 6 g demonstrated the most promising ADMET profiles, characterized by moderate clearance rates, low toxicity potential, and favorable metabolic stability.