The transcriptome contains rich information on molecular, cellular and organismal phenotypes. However, experimental and statistical limitations constrain sensitivity and throughput of genetic screening with single-cell transcriptomics readout. To overcome these limitations, we introduce targeted Perturb-seq (TAP-seq), a sensitive, inexpensive and platform-independent method focusing single-cell RNA-seq coverage on genes of interest, thereby increasing the sensitivity and scale of genetic screens by orders of magnitude. TAP-seq permits routine analysis of thousands of CRISPR-mediated perturbations within a single experiment, detects weak effects and lowly expressed genes, and decreases sequencing requirements by up to 50-fold. We apply TAP-seq to generate perturbation-based enhancer–target gene maps for 1,778 enhancers within 2.5% of the human genome. We thereby show that enhancer–target association is jointly determined by three-dimensional contact frequency and epigenetic states, allowing accurate prediction of enhancer targets throughout the genome. In addition, we demonstrate that TAP-seq can identify cell subtypes with only 100 sequencing reads per cell.