The recent outbreak of coronavirus disease-19 (COVID-19) continues to drastically affect healthcare throughout the world. To date, no approved treatment regimen or vaccine is available to effectively attenuate or prevent the infection. Therefore, collective and multidisciplinary efforts are needed to identify new therapeutics or to explore effectiveness of existing drugs and drug-like small molecules against SARS-CoV-2 for lead identification and repurposing prospects. This study addresses the identification of small molecules that specifically bind to any of the three essential proteins (RdRp, 3CL-protease and helicase) of SARS-CoV-2. By applying computational approaches we screened a library of 4574 compounds also containing FDA-approved drugs against these viral proteins. Shortlisted hits from initial screening were subjected to iterative docking with the respective proteins. Ranking score on the basis of binding energy, clustering score, shape complementarity and functional significance of the binding pocket was applied to identify the binding compounds. Finally, to minimize chances of false positives, we performed docking of the identified molecules with 100 irrelevant proteins of diverse classes thereby ruling out the non-specific binding. Three FDA-approved drugs showed binding to 3CL-protease either at the catalytic pocket or at an allosteric site related to functionally important dimer formation. A drug-like molecule showed binding to RdRp in its catalytic pocket blocking the key catalytic residues. Two other drug-like molecules showed specific interactions with helicase at a key domain involved in catalysis. This study provides lead drugs or drug-like molecules for further in vitro and clinical investigation for drug repurposing and new drug development prospects.