Background: Accessing COVID-19 vaccines is a challenge despite successful clinical trials. This burdens the COVID-19 treatment gap, thereby requiring accelerated discovery of anti-SARS-CoV-2 agents. This study explored the potential of anti-HIV reverse transcriptase (RT) phytochemicals as inhibitors of SARS-CoV-2 non-structural proteins (nsps) by targeting in silico key sites in the structures of SARS-CoV-2 nsps. One hundred four anti-HIV phytochemicals were subjected to molecular docking with nsp3, 5, 10, 12, 13, 15, and 16. Top compounds in complex with the nsps were investigated further through molecular dynamics. The drug-likeness and ADME (absorption, distribution, metabolism, and excretion) properties of the top compounds were also predicted using SwissADME. Their toxicity was likewise determined using OSIRIS Property Explorer. Results: Among the top-scoring compounds, the polyphenolic functionalized natural products comprised of biflavones 1, 4, 11, 13, 14, 15; ellagitannin 9; and bisisoquinoline alkaloid 19 were multi-targeting and exhibited strongest binding affinities to at least two nsps (binding energy = − 7.7 to − 10.8 kcal/mol). The top ligands were stable in complex with their target nsps as determined by molecular dynamics. Several top-binding compounds were computationally druggable, showed good gastrointestinal absorptive property, and were also predicted to be non-toxic. Conclusions: Twenty anti-HIV RT phytochemicals showed multi-targeting inhibitory potential against SARS-CoV-2 non-structural proteins 3, 5, 10, 12, 13, 15, and 16. Our results highlight the importance of polyhydroxylated aromatic substructures for effective attachment in the binding/catalytic sites of nsps involved in post-translational mechanism pathways. As such with the nsps playing vital roles in viral pathogenesis, our findings provide inspiration for the design and discovery of novel anti-COVID-19 drug prototypes. © 2021, The Author(s).