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Dengue virus (DENV) is the causative agent of DENV infection. To tackle DENV infection, the development of therapeutic molecules as direct-acting antivirals (DAAs) has been demonstrated as a truly effective approach. Among various DENV drug targets, non-structural protein 5 (NS5)—a highly conserved protein among the family Flaviviridae—carries the RNA-dependent RNA polymerase (DENV^RdRp) domain at the C-terminal, and its “N-pocket” allosteric site is widely considered for anti-DENV drug development. Therefore, in this study, we developed a pharmacophore model by utilising 41 known inhibitors of the DENV^RdRp domain, and performed model screening against the FDA’s approved drug database for drug repurposing against DENV^RdRp. Herein, drugs complying with the pharmacophore hypothesis were further processed through standard-precision (SP) and extra-precision (XP) docking scores (DSs) and binding pose refinement based on MM/GBSA binding energy (BE) calculations. This resulted in the identification of four potential potent drugs: (i) desmopressin (DS: −10.52, BE: −69.77 kcal/mol), (ii) rutin (DS: −13.43, BE: −67.06 kcal/mol), (iii) lypressin (DS: −9.84, BE: −67.65 kcal/mol), and (iv) lanreotide (DS: −8.72, BE: −64.7 kcal/mol). The selected drugs exhibited relevant interactions with the allosteric N-pocket of DENV^RdRp, including priming-loop and entry-point residues (i.e., R729, R737, K800, and E802). Furthermore, 100 ns explicit-solvent molecular dynamics simulations and end-point binding free energy assessments support the considerable stability and free energy of the selected drugs in the targeted allosteric pocket of DENV^RdRp. Hence, these four drugs, repurposed as potent inhibitors of the allosteric site of DENV^RdRp, are recommended for further validation using experimental assays.