The Savonius rotor, a type of vertical-axis wind turbine, seems to be promising for small-scale power generation. Most of the studies conducted so far have focused on the evaluation of torque and power coefficients (CT, CP) of the rotor. This paper aims at analyzing the aerodynamic drag and lift coefficients (CD, CL) of a Savonius rotor blade profile that is generated by the simplex search method to maximize its CP. The optimization is carried out by coupling the numerical simulations with the simplex search method. The optimized blade profile thus obtained is symmetric about its axis, where one half is created through a natural cubic spline curve using three points. Two-dimensional (2D) unsteady numerical simulations have been conducted by adopting ANSYS FLUENT solver to examine the CD and CL of the optimized blade profile at an inlet air velocity of 7.30 m/s. The shear stress transport (SST) k-ω turbulence model is used to solve the transient Reynolds-averaged Navier-Stokes (RANS) equations. The aerodynamic analysis is performed over a range of tip speed ratios (TSRs). The total pressure, velocity magnitudes, and the turbulent intensity contours of the optimized blade profile are generated and studied at different angles of rotation. The CD and CL of the blade profile are investigated for a complete rotation with an increment of 1°. At TSR = 0.8, the optimized profile shows a CDmax of 1.91 at an angle of rotation of 54°, while CDmin is found to be 0.45 at an angle 147°.