We present HST/WFC3 ultraviolet imaging in the F275W and F336W bands of the Type IIb SN 2001ig at an age of more than 14 years. A clear point source is detected at the site of the explosion, with mF275W = 25.39 0.10 and mF336W = 25.88 0.13 mag. Despite weak constraints on both the distance to the host galaxy NGC 7424 and the line-of-sight reddening to the supernova, this source matches the characteristics of an early B-type main-sequence star with 19,000 < Teff < 22,000 K and . A BPASS v2.1 binary evolution model, with primary and secondary masses of 13 M and 9 M , respectively, is found to simultaneously resemble, in the Hertzsprung-Russell diagram, both the observed location of this surviving companion, and the primary star evolutionary endpoints for other Type IIb supernovae. This same model exhibits highly variable late-stage mass loss, as expected from the behavior of the radio light curves. A Gemini/GMOS optical spectrum at an age of 6 years reveals a narrow He ii λ4686 emission line, indicative of continuing interaction with a dense circumstellar medium at large radii from the progenitor. We review our findings on SN 2001ig in the context of binary evolution channels for stripped-envelope supernovae. Owing to the uncrowded nature of its environment in the ultraviolet, this study of SN 2001ig represents one of the cleanest detections to date of a surviving binary companion to a Type IIb supernova.