Nuclear magnetic resonance (NMR) spectroscopy is a well-established technique for the measurement of intra-diffusion coefficients. Recently, such information has been used as a basis of predictive models to extrapolate to the Fick diffusion coefficient of liquid mixtures. The present work presents a new approach to directly access the Fick diffusion coefficient by spatially resolved NMR experiments. The Fick diffusion coefficient of the binary mixture TEA/H2O was determined at two temperatures, 283.2 K and 275.2 K. The results are consistent with values previously reported either from optical experiments or predictive Darken-type models developed for this system. The proposed methodology adds high-resolution NMR to the toolbox for the study of the transport diffusion of multicomponent mixtures. It is, however, still limited to mixtures with liquid-liquid equilibrium phase separation.