We have measured the low temperature magneto-drag between two two-dimensional electron gases (2DEGs). At matched densities, minima at odd filling factor are observed down to fields at which the Zeeman energy is only one tenth of temperature. At mismatched densities a novel 1/B periodic oscillation in the magneto-drag is observed with frequency h/2e times the density mismatch between the 2DEGs. The oscillation causes negative minima when the filling factor difference between the 2DEGs is odd and positive maxima when it is even. An empirical model is presented that assumes a negative contribution to the drag from electrons with anti-parallel spin in each layer and a positive contribution from electrons with parallel spin. The model faithfully reproduces the experimental results at matched as well as mismatched densities.