Police saw Fernando Vieira de Magalhaes' uninsured Lexus clip the kerb on Brunswick Road, at 7.45pm, on July 22, and they activated their lights.
But he continued driving and when he stopped for a red traffic light, the officers tried to block the Lexus between a bus.
The bus moved and Vieira de Magalhaes drove off, forcing the WPC to move out of the way to avoid contact, prosecutor Zaiban Alam told Sheffield Crown Court, on Friday.
He travelled through two sets of red traffic lights on Burngreave Road at 50mph, and reached 70mph on Norwood Road, when the limits are 30mph.
He completed “several laps of Burngreave Road and Barnsley Road” before officers managed to pen the Lexus in with another bus on Longley Hall Road.
One officer struck him through the open window to distract him and as they snatched the key from the ignition, the defendant hit them on the arm.
As he was dragged from the car he kneed the officer's thigh.
A test revealed he had 41 mcgs in 100 mls of breath when the legal limit is 35 mcgs.
The court heard he has previous convictions for drink driving in August 2012 and April 2019, and received a 41 month ban in December 2019 for driving while disqualified.
Vanessa Saxton, mitigating, said the Portuguese national is HIV positive, suffers from other health conditions and has problems with alcohol and cannabis.
She said he apologises to the court, but added the pursuit was of a short duration and the level of his intoxication was low.
Vieira de Magalhaes, 60, of Longley Hall Road, Sheffield, pleaded guilty to driving dangerously, and driving while disqualified, over the limit and with no insurance.
Judge Graham Reeds QC said: "You've not been to prison before but your driving on this occasion, made worse by your previous sentences, means a custodial sentence is warranted."
He jailed him for 12 months and banned him for five years and six months.