To limit the incidence of relapse, cancer treatments must not promote the emergence of drug resistance in tumour and cancer stem cells. Under the proviso that a therapeutic amount of boron is selectively delivered to cancer cells, Boron Neutron Capture Therapy (BNCT) may represent one approach that meets this requirement. To this end, we report on the synthesis and pharmacology of several chemical entities, based on boron-rich carborane moieties that are functionalised with Delocalized Lipophilic Cations (DLCs), which target selectively the mitochondria of tumour cells. The treatment of tumour and cancer stem cells (CSCs) with such DLC-functionalized carboranes (DLC-carboranes) induces cell growth arrest that is both highly cancer-cell selective and permanent. Experiments involving cultures of normal and cancer cells show that only normal cells exhibit recapitulation of their proliferation potential upon removal of the DLC-carborane treatment. At the molecular level, the pharmacological effect of DLC-carboranes is exerted through activation of the p53/p21 axis.