Background: RNA-dependent RNA polymerase (RdRp) contributes to the transcription cycle of the SARS-CoV-2 virus with the possible assistance of nsp-7-8 cofactors. Objective: To investigate the viral protective effects of complementary drugs in computational approaches that use viral proteins. Methods: For the in silico studies, the identified compounds were subjected to molecular docking with RdRp protein followed by structural and functional analyses, density functional theory (DFT), and molecular dynamics (MD) simulation. The 3D structure of RdRp (6m71 PDB ID) was obtained from the protein databank as a target receptor. After reviewing the literature, 20 complementary and synthetic drugs were selected for docking studies. The top compounds were used for DFT and MD simulation at 200 ns. DFT of the compounds was calculated at B3LYP/6-311G (d, p) based on chemical properties, polarizability, and first-order hyperpolarizability. Results were analyzed using USCF Chimera, Discovery Studio, LigPlot, admetSAR, and mCule. Results: Computational studies confirmed the potent interaction of the complementary drugs forsythiaside A, rhoifolin, and pectolinarin with RdRp. Common potential residues of RdRp (i.e., Thr-556, Tyr-619, Lys-621, Arg-624, Asn-691, and Asp-760) were observed for all three docking complexes with hydrogen bonding. Docking analysis showed strong key interactions, hydrogen bonding, and binding affinities (-8.4 to −8.5 kcal/mol) for these ligands over the FDA-approved drugs (−7.4 to −7.6 kcal/mol). Docking and simulation studies showed these residues in the binding domains. Conclusion: Significant outcomes of novel molecular interactions in docking, simulation, DFT, and binding domains in the structural and functional analyses of RdRp were observed.