Punctuated bursts of protein expression are common in biological systems. Yet whether these exert a lasting influence on future generations is largely unknown. We tested this by transiently overexpressing virtually all open reading frames in Saccharomyces cerevisiae. Strikingly, expression of nearly fifty intrinsically disordered proteins (IDPs) created heritable new traits that persisted after overproduction was stopped. The proteins were strongly enriched in RNA binding proteins (RBPs) and transcription factors (TFs). The inheritance patterns of these traits resembled protein-based genetic elements, known as prions. RBPs control the fate of nearly every transcript in a cell, but no existing approach for studying these post-transcriptional gene regulators combines transcriptome-wide throughput and biophysical precision. We used commonly available hardware to generate a uniform and highly redundant array of RNA transcripts, spanning an entire genome, on an Illumina MiSeq chip. We harnessed this transcribed genome array (TGA) to identify hundreds of new targets of Vts1/Smaug, which coordinates the degradation of maternal RNAs during development and emerged as a robust hit in our screen. This approach provided nucleotide resolution and direct measurements of affinity and dissociation in a single experiment, supplanting prior knowledge of determinants driving Vts1 substrate recognition. Acquisition of the [VTS1+] prion enhanced the decay rates of target mRNAs and expanded the protein’s substrate repertoire. The capacity to self-template was conserved in Drosophila and human Smaug proteins. Our data force a re-examination of the mechanism of Vts1/Smaug-mediated gene regulation, which was thought to occur via binding to 3’-UTRs from a handful of targeted studies. Instead, we found that binding throughout the transcript resulted in target degradation. Moreover, the idealized equimolar binding landscape of the TGA revealed previously unknown roles for Vts1/Smaug in the birth of new genes from proto-ORFs and in the regulation of stress responses. Our findings transform our understanding of Vts1/Smaug function, and have important implications for the many other IDPs involved in eukaryotic gene control.