We present observations of GRB 130831A obtained by Swift, Chandra, and multiple ground-based observatories. This burst shows an uncommon falloff in the X-ray light curve at about 1e+5 s after the trigger, with a decay slope of alpha ~7. The standard Forward Shock model offers no explanation for such a feature. Instead, a model in which the outflow from a newly born magnetar powers the early X-ray emission provides a good description of the data. After the drop, the X-ray afterglow resumes a decay with a slope typical of FS emission. The optical emission, on the other hand, shows no clear break across the X-ray drop and its decay is consistent with that of the late X-rays; we thus believe that the optical and late X-ray emission are both FS. We use our data on GRB 130831A, and the associated SN2013fu, to obtain for the first time the energy breakdown for a SN into non-relativistic ejecta, relativistic ejecta that power the afterglow, and emission from the magnetar outflow.