The girl, who cannot be identified, suffered severe pelvic injuries when she was thrown from the carriage on to the track and had to crawl in agony to a station to raise the alarm.
She also suffered a broken arm and many lesser injuries in Wednesday night's attack, which police are treating as attempted murder. She was "comfortable" in hospital last night.
Det Supt Graham Satchwell of British Transport Police said: "It was a brutal and potentially deadly attack on an innocent young woman travelling alone in very vulnerable circumstances." Officers were searching the track for clues yesterday and examining recordings from security cameras at stations.
The girl was travelling with five or six friends on Wednesday's 21.38 service from East Grinstead to London Victoria on her way home to East Croydon, south London.
She had joined the train at Upper Warlingham just after 10pm. Her friends got off at Sanderstead and it is not clear whether she was left alone in the carriage with her attacker. The train was near South Croydon when the man offered the girl a drink from a can of lager. When she declined, they struggled, the man opened a door and pushed her out.
Police said her attacker was a thin, 6ft tall black man, aged about 28, with short hair, a spotty face and a goatee beard. He had at least one prominent gold tooth. He was wearing a green and white check shirt, blue jeans and white trainers.