Biological and dynamic mechanisms by which Drug-tolerant persister (DTP) cells contribute to the development of acquired drug resistance have not been fully elucidated. Here, by integrating multidimensional data from drug-treated PC9 cells, we developed a novel multiscale mathematical model from an evolutionary perspective that encompasses epigenetic and cellular population dynamics. By coupling stochastic simulation with quantitative analysis, we identified epigenetic instability as the most prominent kinetic feature related to the emergence of DTP cell subpopulations and the effectiveness of intermittent treatment. Moreover, we revealed the optimal schedule for intermittent treatment, including the optimal area for therapeutic time and drug holidays. By leveraging single-cell RNA-seq data characterizing the drug tolerance of lung cancer, we validated the predictions made by our model and further revealed previously unrecognized biological features of DTP cells, such as cell autophagy and migration, as well as new biomarker genes of therapeutic tolerance. Our work not only provides a paradigm for the integration of multiscale mathematical models with newly emerging genomics data but also improves our understanding of the crucial roles of DTP cells and offers guidance for developing new intermittent treatment strategies against acquired drug resistance in cancer.