A new and strikingly simple procedure for deriving universal formulae for correlation functions in a broad class of models is presented. Physics applications include double-scaled random matrix models, low-dimensional models of gravity and supergravity, various string theories, and the low-temperature, near-horizon quantum dynamics certain black holes. Mathematical applications include computations in intersection theory on the compactified moduli space of (super)Riemann surfaces of genus g and n boundaries, as well as evaluations of its volume. In certain supersymmetric cases, the techniques used provide swift derivations of some remarkable closed-form formulae from the mathematical literature, and readily yield new closed-form expressions.