Machining of advanced material like Inconel-718 with accuracy and precision is an emerging need. Selection of an appropriate optimal range of cutting parameters is quite essential to achieve high-quality cut and is a challenging task within this domain of study. The aim of this research is to develop a robust prediction model which can suggest the desired range of cutting parameters for accomplishing better cutting quality, precision, and geometrical accuracy. Experiments have been performed on a 300-W (CNC-PCT 300) pulsed Nd:YAG laser cutting system at various levels of input cutting parameters, viz. gas pressure, standoff distance, cutting speed and laser power. Thereafter, response surface methodology has been adopted to develop mathematical models in terms of aforementioned input cutting parameters for geometrical quality characteristics: Top Kerf Width (TKW) and Bottom Kerf Width (BKW). The percentage error in the prediction models has been found as 1.981% and 1.511% for TKW and BKW, respectively. These developed models have been validated by comparing the predicted values with the experimental ones. Further, these models have been used to determine the dependency of responses on input parameters and to ascertain an optimal range of cutting parameters pertaining to better quality cut with high precision and geometrical accuracy. Moreover, it has also been found that the dependency of input parameters on output is non-monotonous in nature.