Kachenga Kabwe sped off and drove through red lights in the Harehills area of the city after officers spotted her driving on the wrong side of the road.
Leeds Crown Court heard officers followed Kabwe after they saw her driving towards them in the wrong carriageway on Harehills Lane at 10pm on October 6 this year.
Carmel Pearson, prosecuting, told Leeds Crown Court how a car had to swerve out of the way to avoid a head-on collision.
The 51-year-old initially pulled over near to the central reservation when officers indicated for her to stop.
Miss Pearson said Kabwe appeared to be co-operative and wound down a window to speak to an officer.
Kabwe was told to park away from the central reservation but instead drove off.
She drove above the speed limit in busy residential areas and went through red lights on Compton Road and Foundry Approach.
The incident lasted four-and-a-half minutes before Kabwe stopped.
A breath test showed she was more than double the drink-drive limit.
Kabwe, of Wykebeck Street, Osmondthorpe, pleaded guilty to dangerous driving, drink driving and failing to stop.
Kara Frith, mitigating, said Kabwe had no previous convictions and was ashamed of what she had done.
She said Kabwe had been to a surprise birthday party and took the decision to drive as others were relying on her for a lift.
Miss Frith said: "She has never been in trouble before. It really was a moment of madness."
"She has not driven since and she is mortified at what happened."
Miss Firth said Kabwe worked as a nurse and was closely involved with her local church and the Leeds Zambian Community Association.
Kabwe was given a four-month prison sentence, suspended for 12 months.
She was also ordered to do 160 hours of unpaid work and was banned from driving for two years.
Judge Neil Clark said: "You know how dangerous it is to go through red lights and break speed limits.
"Being a nurse you would have seen people injured from this at times.
"You are an unusual defendant for many reasons.
"You are a perfectly respectable woman, 51 years of age and have never been in trouble with the courts before.
"You are a church goer and you are a hard-working nurse.
"Driving of this nature normally attracts an immediate custodial sentence.
"I can't imagine you will do anything like this again in your life."