Cellular memory describes the length of time a particular transcriptional state exists at the single-cell level. Transcriptional states with memory can underlie important processes in biology, including therapy resistance in cancer. Here we present a new experimental and computational approach for identifying gene expression states with memory at single-cell resolution by combining single-cell RNA sequencing (scRNA-seq) with cellular barcoding. With this technique, we can systematically quantify the full expression profile of these memory states as well as their population dynamics including the relative growth rates of cells within different states and the rates of switching between states. We applied this approach to human melanoma cells and uncovered memory gene expression states that are predictive of which cells will be resistant to combination BRAF and MEK inhibition. While these cells have not been treated with targeted therapies, they already express markers of resistance, and thus are referred to here as “primed” for resistance. From the scRNA-seq data alone, the drug-susceptible and primed cells appear as two distinct and unrelated cell populations. From the lineage barcodes, we found that most cells remain within the same state, demonstrating memory of gene expression. However, we also directly observe state switching as we find that about 18% of lineages contain cells that have switched states. While the molecular drivers of state switching are not immediately apparent from scRNA-seq data alone, we specifically analyzed lineages that undergo state switching and identified TGF-β and PI3K as drivers of state switching at the single-cell level. Through functional validation and single-cell RNA-sequencing, we show mechanistic single-cell manipulation of state switching that ultimately yields changes in cellular phenotype. We leverage these mechanisms of state switching to delay resistance by demonstrating that reducing the number of primed cells with a PI3K inhibitor prior to BRAF and MEK inhibition ultimately leads to fewer resistant colonies. Our results show that modulation of cellular signaling can globally regulate gene expression programs to overcome therapy resistance.