Greg Oden -- Blasted Ex-Gf with THREE Shots to the Face ... According to Police Report

Greg Oden allegedly flew into a booze-fueled rage, and punched his estranged girlfriend in the face THREE times before calling police to report himself.

Details of Oden's arrest last week were just released by cops in Marion County, Indiana -- and it paints a brutal picture. The girlfriend told police she and Oden had been at a nightclub where she says he'd been drinking shots and beers ... and when they got home things turned violent.

According to the docs ... Oden grabbed her and shoved her onto the couch ... and then started throwing "closed fist" punches to her face. The woman says he hit her 3 times -- once in the left eye, once in the forehead, and once in the nose.

She says the shot to her forehead opened a gash from which she started bleeding -- and Greg stopped attacking once he saw the blood. The victim was hospitalized and had to get 3 stitches between her eyebrows, and suffered a broken nose.

In the docs, a friend who was in the house says she overheard some talk of the girlfriend possibly cheating on Greg ... which might have sparked the fight.