Faizaan Bashir put pedestrians in danger as he mounted pavements in a bid to escape officers during the incident..
The West Yorkshire Police helicopter was also deployed during the ten-minute pursuit after Bashir was spotted in a stolen Toyota Yaris.
Leeds Crown Court heard officers saw the vehicle on Bradford Road, Batley, at 8.50pm on September 4, 2017.
Bashir, aged 17 at the time, ignored red lights and drove above the speed limit as he headed towards Dewsbury.
He drove past Dewsbury police station at 60mph, drove the wrong way on a one-way street and mounted kerbs.
The teenager, who had a passenger in the car, caused other drivers to take evasive action and turned his lights off.
Andrew Horton, prosecuting, said the pursuit ended when Bashir crashed into bollards on Sackville Street.
He ran from the vehicle but was tracked with the help of the police helicopter and arrested at 11pm.
Bashir told police he had just finished work and said: "I will save you time - I'm drunk."
A roadside breath test showed he was almost one-and-a-half times the drink drive limit.
He refused to provide a further breath sample when he was taken to a police station.
Police found a vodka bottle with his fingerprints on it in the car.
Bashir, now 19, pleaded guilty to dangerous driving.
Probation officer Mick Berry said Bashir's drinking interfered with his education, which he completed at the age of 16.
He described Bashir, of Kingfisher Crescent, Dewsbury, as "utterly indifferent to what he has done" and suggested he was only "paying lip service" to the court.
Geraldine Kelly, mitigating, said Bashir was sorry for what he had done and appreciated he could have seriously injured someone.
She said the defendant was on a "downward spiral" at the time but now works full time in his family's bedding factory.
Judge Tom Bayliss QC sentenced Bashir to six months in a young offender institution.
He also disqualified him from driving for two years and two months.
The judge said: "You put yourself at risk, you put your passenger at risk, you put other drivers at risk, you put other pedestrians at risk and you put the police at risk."