A novel combinatorial approach including computer-aided simulation and robust statistical data-based methods was introduced to intensify the chemical absorption process of H2S by diethanolamine (DEA) from sour industrial off-gas. Effects of three parameters (lean amine H2S impurity (LAHI), lean amine temperature (LAT) and column pressure (CP) on the alteration trends and sensitivity of H2S removal were studied using response surface methodology (RSM) and Sobol’s sensitivity analysis (SA). Then, the optimal conditions for maximizing the H2S removal were determined. Results depicted that H2S removal will be decreased at higher LAHI and LAT. SA showed that LAHI (83%) was the most impactful factor on H2S removal. LAT (15%) and CP (2%) showed a relatively-low and negligible effects on the removal efficiency, respectively. It was shown that low impact of LAT and CP on H2S removal arised from weak variations of thermodynamic parameters of H2S absorption (H2S solubility, equilibrium constant, and enthalpy of absorption) with those factors. Maximum H2S removal of 99.995% was resulted at the optimal values of LAHI = 0.01 molH2S/molDEA, LAT = 53.7 °C, and CP = 1500 kPa.