Recent advances in single-cell transcriptomics are ideally placed to unravel intratumoral heterogeneity and selective resistance of cancer stem cell (SC) subpopulations to molecularly targeted cancer therapies. However, current single-cell RNA-sequencing approaches lack the sensitivity required to reliably detect somatic mutations. We developed a method that combines high-sensitivity mutation detection with whole-transcriptome analysis of the same single cell. We applied this technique to analyze more than 2,000 SCs from patients with chronic myeloid leukemia (CML) throughout the disease course, revealing heterogeneity of CML-SCs, including the identification of a subgroup of CML-SCs with a distinct molecular signature that selectively persisted during prolonged therapy. Analysis of nonleukemic SCs from patients with CML also provided new insights into cell-extrinsic disruption of hematopoiesis in CML associated with clinical outcome. Furthermore, we used this single-cell approach to identify a blast-crisis-specific SC population, which was also present in a subclone of CML-SCs during the chronic phase in a patient who subsequently developed blast crisis. This approach, which might be broadly applied to any malignancy, illustrates how single-cell analysis can identify subpopulations of therapy-resistant SCs that are not apparent through cell-population analysis.