Calvin Smith reached speeds of up to 60mph in a 30mph zone after being spotted driving in Belle Isle on May 7 this year.
Leeds Crown Court heard the pursuit ended when the 21-year-old leapt from the car and crashed into a parked vehicle.
Dave Mackay, prosecuting, said Smith forced his way through traffic on Belle Isle Road, narrowly avoiding a collision.
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He hit the kerb and lost a wheel trim as he drove around Belle Isle Circus and back onto Belle Isle Road.
He was chased and arrested as he tried to jump over a fence.
Smith, of Wykebeck Avenue in Leeds, pleaded guilty to dangerous driving, driving without insurance and driving without a licence.
Stephen Welford, mitigating, said Smith had no previous convictions.
Probation officer Mick Berry said Smith, who has eight brothers and sisters, has no qualifications and displayed "limited motivation".
Smith was given a six month jail sentence, suspended for 18 months. He was banned from driving for two years.
He was also ordered to complete a 15-day rehabilitation activity requirement and 200 hours of unpaid work.