DNA damage can activate apoptotic and non-apoptotic forms of cell death; however, it remains unclear what features dictate which type of cell death is activated. We report that p53 controls the choice between apoptotic and non-apoptotic death following exposure to DNA damage. In contrast to the conventional model, which suggests that p53-deficient cells should be resistant to DNA damage-induced cell death, we find that p53-deficient cells die at high rates following DNA damage, but exclusively using non-apoptotic mechanisms. Our experimental data and computational modeling reveal that non-apoptotic death in p53-deficient cells has not been observed due to use of assays that are either insensitive to cell death, or that specifically score apoptotic cells. Using functional genetic screening - with an analysis that enables computational inference of the drug-induced death rate - we find in p53-deficient cells that DNA damage activates a mitochondrial respiration-dependent form of cell death, called MPT-driven necrosis. Cells deficient for p53 have high basal respiration, which primes MPT-driven necrosis. Finally, using metabolite profiling, we identified mitochondrial activity-dependent metabolic vulnerabilities that can be targeted to potentiate the lethality of DNA damage specifically in p53-deficient cells. Our findings reveal how the dual functions of p53 in regulating mitochondrial activity and the DNA damage response combine to facilitate the choice between apoptotic and non-apoptotic death.