For several decades, it has been hypothesized that Alfvén waves are responsible for accelerating a significant fraction of auroral electrons. Satellite data show Alfvén waves deposit sufficient energy in the auroral zone to produce auroras. Modeling of the auroral zone has suggested Alfvén waves are capable of resonantly accelerating a significant number of electrons to auroral energies. Using the Large Plasma Device, a collaborative research facility at UCLA funded by DOE and NSF, we launch inertial Alfvén waves in plasma conditions relevant to the auroral zone and simultaneously collect measurements of the electron velocity distribution that resolve changes on the timescale of the Alfvén wave period. Alfvén wave propagation through the LAPD is recorded using Elsässer probes that measure the perpendicular electric and magnetic fields of the wave. The electron velocity distribution is measured using wave absorption, a technique where the resonant absorption of a small-amplitude whistler-mode wave is used to determine the phase-space density of electrons. Using the field-particle correlation technique, measurements of the electron velocity distribution are found to contain a velocity-space signature of electrons gaining energy from the Alfvén wave via Landau resonance. This interpretation of measurements is supported by gyrokinetic simulation, analytic kinetic theory, and Liouville mapping of a test particle distribution through the Alfvén wave. The energy gain per electron per second resulting from the resonant acceleration measured in the laboratory is comparable to an estimate in the auroral zone. The experiment, theory, and simulations are the first demonstration of a clear causal relationship between Alfvén waves and accelerated electrons that directly cause auroras.