Quantitative structure property relationship (QSPR) is a computational modeling approach that correlates the chemical structure of compounds with their physicochemical or biological properties. Accurate estimation of physicochemical and other biological parameters of drug molecules is a critical factor in drug discovery. In the present work, we developed a graph-based QSPR model for molecular structures which employed molecular structural invariants as predicting features. Degree and distance topological indices were derived from molecular graphs and combined with random forest (RF), gradient boosting, and multiple line regression (MLR) for prediction of predictive performance on the diverse drug datasets. The proposed RF model obtained an approximate 18–25% improvement in $R^2$ and a reduction of about 30% in RMSE over the classical linear regression models, showing better generalization performance. In the context of drug screening, the model accurately predicted early physicochemical properties including molar refractivity and polarizability, rendering it a tool to assess rapidly compounds for neurological and anticancer therapeutics. In addition, the computational model was about 15 times faster on average than existing QSPR approaches, achieving its excellent efficiency and applicability. The final results demonstrated that the molecular structural invariants functioned as good descriptors for generating reliable, interpretable, and predictive QSPR models relevant to early-stage drug discovery.