Police say the 24-year-old would have been raped if she had not managed to escape after being grabbed by a man in Pendas Way, Cross Gates, at about 9.35pm.
The woman had got off a Number 40 bus from Leeds when she was pulled into a ginnel near the junction with Pendas Grove.
The attacker tried to pull her leggings down but she fought back and he ran off in the direction of John Smeaton Academy.
Detective Chief Inspector Lisa Atkinson, Head of Leeds District Reactive CID, said: “This was a frightening experience for the victim who has been left very badly shaken by what happened. We believe the offender would have gone on to seriously sexually assault her if she hadn’t fought back.
“The victim is being supported by specialist officers and we are carrying out extensive enquiries to trace this man. The scene of the incident has undergone a forensic examination.
“We would like to hear from anyone who was in the area around the time and saw a man fitting this description either before or after the incident.”
The man was described as white, about 5ft 9ins tall, of medium build and aged in his late thirties. He had short or shaved hair, short stubble on his face, a skinny nose and was said to have a head that was small for his body.
He was wearing a scruffy dark-coloured hooded top with the hood up and possibly tracksuit bottoms.
Police said the incident is not being linked to the rape of an 18-year-old woman in Beeston Road, Beeston, last month.
Det Chief Insp Atkinson said: “We have liaised with detectives that are investigating the attempted murder and serious sexual assault in Beeston and at this stage these offences are not being linked.
“We appreciate this incident will understandably cause concern in the community but we would like to reassure people that we are doing everything we can to identify the suspect.
“Officers from the local neighbourhood policing team will be carrying out increased patrols in the area and our advice to people is the same as it would be at any other time. “People should always think carefully about their personal safety when out a night. Ideally don’t walk alone and stick to well-lit areas.”
Anyone with any information that could assist the investigation is asked to contact Leeds District CID via 101 or call the independent crime-fighting charity Crimestoppers anonymously on 0800 555 111.