Data are accumulating on the hydrolytic activity of serum albumin towards esters and organophosphates. Previously, with the help of the technology of proton nuclear magnetic resonance (1H NMR) spectroscopy, we observed the yield of acetate in the solution of bovine serum albumin and p-nitrophenyl acetate (NPA). Thus, we showed that albumin possesses true esterase activity towards NPA. Then, using the methods of molecular docking and molecular dynamics, we established site Sudlow I as the catalytic center of true esterase activity of albumin. In the present work, to expand our understanding of the molecular mechanisms of albumin pseudoesterase and true esterase activity, we investigated—in experiments in vitro and in silico—the interaction of anticoagulant warfarin (WRF, specific ligand of site Sudlow I) and benzodiazepine diazepam (DIA, specific ligand of site Sudlow II) with albumins of different species, and determined how the binding of WRF and DIA affects the hydrolysis of NPA by albumin. It was found that the characteristics of the binding modes of WRF in site Sudlow I and DIA in site Sudlow II of human (HSA), bovine (BSA), and rat (RSA) albumins have species differences, which are more pronounced for site Sudlow I compared to site Sudlow II, and less pronounced between HSA and RSA compared to BSA. WRF competitively inhibits true esterase activity of site Sudlow I towards NPA and does not affect the functioning of site Sudlow II. Diazepam can slow down true esterase activity of site Sudlow I in noncompetitive manner. It was concluded that site Sudlow I is more receptive to allosteric modulation compared to site Sudlow II.