The incident came to light around 9:15 pm when a passerby saw the woman lying on a road and called the police.The victim had gone to Vrindavan on December 22 and was returning home on Wednesday.
She met Verma there and he accompanied her in a car to her hometown. On the way, Verma's two friends joined them.
"She told us that she was gagged, sedated and raped by the trio. They took turns to rape her. A medical examination has confirmed rape," a senior police official said.
Police said she was conscious and taken to AIIMS where she is undergoing treatment.
A case of gang-rape under section 376(G) has been registered.
One of the accused identified as Dilip Verma has been detained.
Delhi Police spokesperson Rajan Bhagat said Verma was picked up from Agra and he is being brought to Delhi for interrogation. He claimed that he knows the victim for five years.
Three teams have been formed and are raiding several places to catch the other two accused.
A senior police official said it is claimed that the woman had earlier tried to get a rape case registered in Agra but after investigations, police did not file any case as they found the allegations to be false.
Police was verifying it.