Lindsey Reed was arrested after a support worker spotted her having sex with a man in the grounds of a hostel in the Hyde Park area.
Leeds Crown Court heard the staff member approached the pair and told them to stop.
Reed and the man ignored the woman and continued having sex for a further 20 minutes until police arrived.
The woman provided a statement to the court in which she described feeling shocked and outraged at their behaviour.
The pair continued having sex when officers arrived and the man became abusive when they were told to stop.
The man told officers: "I will knock you out. Do you want knocking out?"
Officers noted that Reed and the man both appeared unsteady on their feet and appeared to be under the influence of alcohol.
The man assaulted three officers as he was arrested.
Reed was detained without difficulty during the incident at 8.30pm on August 23 this year.
Reed was interviewed about the incident and said she had drank five vodka and cokes and met the defendant through a "mutual friend."
She said she was "not particularly aware" of the location where they were having sex.
At the time of the offence Reed was the subject of a suspended sentence order.
Reed, 29, of Cartmell Drive, Halton Moor, pleaded guilty to outraging public decency and breach of a suspended sentence order.
The court heard she had failed to carry out unpaid work which was a condition of the suspended sentence.
Probation officer Mike Cooper told the court: "She is clearly embarrassed about the whole situation."
Mr Cooper said the offence took place after the mum-of-three had been drinking all day with friends.
Rachel Smith, mitigating, said Reed had not completed the unpaid work due to suffering a hip and ankle injury.
Judge Simon Batiste adjourned the hearing for seven days to allow Reed to obtain medical evidence to support her claim.
She was jailed for five months after Reed returned to court without appropriate evidence.
The man who had sex with Reed was given a four-week prison sentence by magistrates after pleading guilty to outraging public decency, assaulting an emergency worker and being drunk and disorderly.