Integrating single-cell trajectory analysis with pooled genetic screening could reveal the genetic architecture that guides cellular decisions in development and disease. We applied this paradigm to probe the genetic circuitry that controls epithelial-to-mesenchymal transition (EMT). We used single-cell RNA sequencing to profile epithelial cells undergoing a spontaneous spatially determined EMT in the presence or absence of transforming growth factor-β. Pseudospatial trajectory analysis identified continuous waves of gene regulation as opposed to discrete 'partial' stages of EMT. KRAS was connected to the exit from the epithelial state and the acquisition of a fully mesenchymal phenotype. A pooled single-cell CRISPR-Cas9 screen identified EMT-associated receptors and transcription factors, including regulators of KRAS, whose loss impeded progress along the EMT. Inhibiting the KRAS effector MEK and its upstream activators EGFR and MET demonstrates that interruption of key signaling events reveals regulatory 'checkpoints' in the EMT continuum that mimic discrete stages, and reconciles opposing views of the program that controls EMT.