In this paper, a control-based approach to replace the conventional method to achieve accurate indentation quantification is proposed for nanomechanical measurement of live cells using atomic force microscope. Accurate indentation quantification is central to probe-based nanomechanical property measurement. The conventional method for in-liquid nanomechanical measurement of live cells, however, fails to accurately quantify the indentation as effects of the relative probe acceleration and the hydrodynamic force are not addressed. As a result, significant errors and uncertainties are induced in the nanomechanical properties measured. In this paper, a control-based approach is proposed to account for these adverse effects by tracking the same excitation force profile on both a live cell and a hard reference sample through the use of an advanced control technique, and by quantifying the indentation from the difference of the cantilever base displacement in these two measurements. The proposed control-based approach not only eliminates the relative probe acceleration effect with no need to calibrate the parameters involved, but it also reduces the hydrodynamic force effect significantly when the force load rate becomes high. We further hypothesize that, by using the proposed control-based approach, the rate-dependent elastic modulus of live human epithelial cells under different stress conditions can be reliably quantified to predict the elasticity evolution of cell membranes, and hence can be used to predict cellular behaviors. By implementing the proposed approach, the elastic modulus of HeLa cells before and after the stress process were quantified as the force load rate was changed over three orders of magnitude from 0.1 to 100 Hz, where the amplitude of the applied force and the indentation were at 0.4-2 nN and 250-450 nm, respectively. The measured elastic modulus of HeLa cells showed a clear power-law dependence on the load rate, both before and after the stress process. Moreover, the elastic modulus of HeLa cells was substantially reduced by two to five times due to the stress process. Thus, our measurements demonstrate that the control-based protocol is effective in quantifying and characterizing the evolution of nanomechanical properties during the stress process of live cells.