We investigated the 238U(d,p) reaction as a surrogate for the n + 238U reaction. For this purpose we measured for the first time the gamma-decay and fission probabilities of 239U* simultaneously and compared them to the corresponding neutron-induced data. We present the details of the procedure to infer the decay probabilities, as well as a thorough uncertainty analysis, including parameter correlations. Calculations based on the continuum-discretized coupled-channels and distorted-wave Born approximations were used to correct our data from detected protons originating from elastic and inelastic deuteron breakup. In the region where the fission and gamma-decay probabilities compete, the corrected fission probability is in agreement with neutron-induced data, whereas the gamma-decay probability is much higher than the neutron-induced data. The performed statistical-model calculations are not able to explain these results.