The victim had been out with a friend in Headingley where they met two men who gave them a lift into the city centre in a car.
Later, in the early hours of Sunday, the two women went to Boar Lane to catch a bus home when the same two men approached them in the same car and offered them a lift.
The friend was dropped off in Stanningley before the victim was driven to an unknown address where she was subjected to a serious sexual assault.
Police have released a CCTV image of a man they want to identify in connection with the attack. He is described as white, 6ft, aged in his late-20s with short dark hair. He wore a grey top, jeans and grey trainers.
“Detective Inspector Phil Jackson, of Leeds District CID, said: “We are carrying out extensive enquiries to trace the men and the vehicle involved and to establish the full circumstances of this incident.
“We would like to hear from anyone who recognises this man or who has any information that could assist the investigation.”