Nucleic acids, DNA and RNA, provide important fingerprint information for various pathogens and have significant diagnostic value; however, improved approaches are urgently needed to enable rapid detection of nucleic acids in simple point-of-care formats with high sensitivity and specificity. Here, we present a system that utilizes a series of toehold-triggered hybridization/displacement reactions that are designed to convert a given amount of RNA molecules (i.e., the analyte) into an amplified amount of signaling molecules without any washing steps or thermocycling. Fluorescent probes for signal generation were designed to consume products of the catalytic reaction in order to push the equilibrium and enhance the assay fold amplification for improved sensitivity and reaction speed. The system of toehold-assisted reactions is also modeled to better understand its performance and capabilities, and we empirically demonstrate the success of this approach with two analytes of diagnostic importance, i.e., influenza viral RNA and a micro RNA (miR-31). We also show that the amplified signal permits using a compact and cost-effective smartphone-based fluorescence reader, an important requirement toward a nucleic-acid-based point-of-care diagnostic system.