Transiting planets around rapidly rotating stars are not amenable to precise radial velocity observations, such as are used for planet candidate validation, as they have wide, rotationally broadened stellar lines. Such planets can, however, be observed using Doppler tomography, wherein stellar absorption line profile distortions during transit are spectroscopically resolved. This allows the validation of transiting planet candidates and the measurement of the stellar spin-planetary orbit (mis)alignment, which is an important statistical probe of planetary migration processes. We present Doppler tomographic observations that provide direct confirmation of the hot Jupiter Kepler-13 Ab and also show that the planet has a prograde, misaligned orbit with lambda = 58.degrees6 + or - 2.degrees0. Our measured value of the spin-orbit misalignment is in significant disagreement with the value of lambda = 23degrees + or - 4degrees previously measured by Barnes et al. (2011) from the gravity-darkened Kepler light curve. We also place an upper limit of 0.75 M sub(middot in circle) (95% confidence) on the mass of Kepler-13 C, the spectroscopic companion to Kepler-13 B, which is the proper-motion companion of the planet host star Kepler-13 A.