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. An incident in these circumstances we would normally expect to be fatal."
Officers were searching the track for clues yesterday and examining recordings from security video cameras at stations along the route.
The girl was travelling with friends on Wednesday's 21.38 service from East Grinstead to London Victoria on her way home to East Croydon, south London.
She and five or six friends 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 station 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 from the train. Police are anxious to speak to any passengers on the train and to trace two men who helped the girl when she crawled to the station platform.
They said her attacker was a thin, 6ft tall black man, aged about 28, with short hair, a spotty face and a goatee beard. He appeared to have at least one prominent gold tooth. He was wearing a green and white checked shirt, blue jeans and white trainers.Reuse content