The driver identified as Shiv Kumar Yadav (32) hails from Mathura, UP, and the car in which the crime took place was recovered from the city late last night.
Several Delhi Police teams are on a hunt to track him down in Delhi, Haryana and UP.
The incident took place at around 9:30 PM on Friday when the woman, who works for a finance company in Gurgaon, was headed back to her home in north Delhi's Inderlok area.
On the way, the woman dozed off on the back seat of the car only to wake up and find that they had stopped at a secluded spot. She found that the car doors were locked and, when she tried to raise an alarm, the driver thrashed her and then committed rape, police said.
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A case has been registered at Sarai Rohilla Police Station under Sections 376 (rape), 323 (voluntarily causing hurt) and 506 (criminal intimidation) of IPC.
Meanwhile, the US-based cab service provider, which has come under attack for allegedly flouting norms, has issued a statement saying they are providing all help to police in the investigation.
"Our thoughts are with the victim of this terrible crime and we are working with police as they investigate.We will assist them in any way we can. It is also our policy to immediately suspend a driver's account following allegations of a serious incident, which we have done.