Binarity is believed to dramatically affect the history and geometry of mass loss in AGB and post-AGB stars, but observational evidence of binarity is sorely lacking. As part of a project to search for hot binary companions to cool AGB stars using the GALEX archive, we discovered a late-M star, Y Gem, to be a source of strong and variable UV and X-ray emission. Here we report UV spectroscopic observations of Y Gem obtained with the that show strong flickering in the UV continuum on time-scales of ≲ 20 s, characteristic of an active accretion disk. Several UV lines with P-Cygni-type profiles from species such as Si IV and C IV are also observed, with emission and absorption features that are red- and blue-shifted by velocities of ~500 km s from the systemic velocity. Our model for these (and previous) observations is that material from the primary star is gravitationally captured by a companion, producing a hot accretion disk. The latter powers a fast outflow that produces blue-shifted features due to absorption of UV continuum emited by the disk, whereas the red-shifted emission features arise in heated infalling material from the primary. The outflow velocities support a previous inference by Sahai et al. (2015) that Y Gem's companion is a low-mass main-sequence star. Blackbody fitting of the UV continuum implies an accretion luminosity of about 13 , and thus a mass-accretion rate> 5 × 10 yr; we infer that Roche lobe overflow is the most likely binary accretion mode for Y Gem.