Glioblastomas are among the most lethal cancers, with a five year survival rate below 25%. Temozolomide is typically used in glioblastoma treatment; however, the enzymes APNG and MGMT efficiently mediate the repair of DNA damage caused by temozolomide, reducing treatment efficacy. Consequently, APNG and MGMT inhibition has been proposed as a way of overcoming chemotherapy resistance. Here, we develop a mechanistic mathematical model that explicitly incorporates the effect of chemotherapy on tumor cells, including the processes of DNA damage induction, cell arrest and DNA repair. Our model is carefully parameterized and validated, and then used to virtually recreate the response of heteroclonal glioblastoma to dual treatment with TMZ and inhibitors of APNG/MGMT. Using our mechanistic model, we identify four combination treatment strategies optimized by tumor cell phenotype, and isolate the strategy most likely to succeed in a pre-clinical and clinical setting. If confirmed in clinical trials, these strategies have the potential to offset chemotherapy resistance in glioblastoma patients, and improve overall survival.