Cell response heterogeneity upon treatment is a main obstacle in preclinical development of efficacious cancer drugs, due to the emergence of drug-tolerant cells. We have previously developed a single-cell pipeline called Fate-seq to profile drug-tolerant persisters, based on predictions of their drug response. To automatize and increase the prediction throughput, we present a mathematical framework, composed of machine-learning classification models augmented by an ODE model. First, an ODE model of the extrinsic apoptosis initiation by death ligands is calibrated on time trajectories of hundreds of treated clonal HeLa cells. The resulting deterministic systems are then analysed, based on drug response, to highlight mechanistic features with predictive values for cell decision. In a second step, we combine the predictions of the ODE system with machine-learning classification models to determine the drug response of each cell before it commits to an irreversible decision that would alter their states before profiling. Here we show that the ODE model analysis could detect the time of cell decision shortly after treatment, thanks to the emergence of an additional regulation at the receptor level in drug-sensitive cells. Moreover, the parameters distribution of the deterministic system provided a biological threshold that allows the prediction of cell response. Our mechanistic-informed approach, combining our ODE system with machine learning classifiers, outperformed classic machine learning approaches and enabled the accurate cell response prediction of otherwise unpredictable cells (Meyer et al., Cell Systems 2020).