Target-induced DNA strand displacement is an excellent candidate for developing analyte-responsive DNA circuitry to be used in clinical diagnostics and synthetic biology. While most available technologies rely on DNA circuitry free to diffuse in bulk, here we explore the use of liposomes as scaffolds for DNA-based sensing nanodevices. Our proof-of-concept sensing circuit responds to the presence of a model target analyte by releasing a DNA strand, which in turn activates a fluorescent reporter. Through a combination of experiments and coarse-grained Monte Carlo simulations, we demonstrate that the presence of the membrane scaffold accelerates the process of oligonucleotide release and suppresses undesired leakage reactions, making the sensor both more responsive and robust.