We present a new method for inferring the gravitational potential of the Galactic disk, using the time-varying structure of a phase-space spiral in the (z, w)-plane (where z and w represent vertical position and vertical velocity). Our method of inference extracts information from the shape of the spiral and disregards the bulk density distribution that is usually used to perform dynamical mass measurements. In this manner, it is complementary to traditional methods that are based on the assumption of a steady state. Our method consists of fitting an analytical model for the phase-space spiral to data, where the spiral is seen as a perturbation of the stellar number density in the (z, w)-plane. We tested our method on one-dimensional simulations, which were initiated in a steady state and then perturbed by an external force similar to that of a passing satellite. We were able to retrieve the true gravitational potentials of the simulations with high accuracy. The gravitational potential at 400-500 parsec distances from the disk mid-plane was inferred with an error of only a few percent. This is the first paper of a series in which we plan to test and refine our method on more complex simulations, as well as apply our method to Gaia data.