In this work, the flow of power-law fluids past a solid sphere with and without radial mass flux has been investigated numerically using a finite difference method based SMAC-implicit algorithm implemented on a spherical staggered grid arrangement. It is clearly shown that the flow and drag phenomena are strongly affected by the pertinent dimensionless parameters like Reynolds number (Re), power-law index (n) and the radial mass flux (phi). The effect of suction (phi < 0) on the flow profile is seen to be strong at high Reynolds numbers in the case of shear-thinning fluids (n < 1), whereas the reverse is seen in Newtonian and shear-thickening fluids (n >= 1). On the other hand, irrespective of the value of power-law index, the effect of injection (phi > 0) on the flow profile is significant at all Reynolds numbers. Regardless of the value of the power-law index, the pressure drag coefficient decreases as the value of phi decreases. On the other hand, the friction and total drag coefficients decrease as the value of phi decreases for Newtonian and shear-thinning fluids, whereas an opposite trend is seen in shear-thickening fluids. However, the total drag coefficient is reduced for suction (phi < 0) and augmented for injection (phi > 0) compared to that in the absence of radial mass flux. This is so for all values of power-law index. The present numerical results have been correlated empirically, thereby enabling the prediction of the drag coefficient (hence terminal velocity) in a new application.