Matthew Kenny, 24, from Huddersfield, took his brother’s Subura Imprezza out with Curt Gorog, 29, of no fixed abode, while uninsured on March 13 last year.
Police officers saw the car travelling at speed on Moor Top Lane, in Huddersfield, but Kenny sped away, travelling at up to 100mph through 30mph zones.
He was clocked at 109mph in a 50mph zone near the Grange Moor roundabout.
While evading officers, Gorog emptied a large box of loose cannabis from the window.
The 10-minute pursuit ended when Kenny, who was also under the influence of alcohol, lost control of the car in Blacker Lane, Netherton, Wakefield.
Kenny, who was on bail over drug offences at the time of the pursuit, pleaded guilty to possession with intent to supply, aggravated vehicle taking, dangerous driving and driving while over the prescribed limit on July 27.
He has been sentenced to a total of three years in prison to run consecutive to a 26 month sentence he is already serving for burglary and drugs matters.
Gorog pleaded guilty to assisting an offender with regards to throwing the cannabis out of the car to impede the police investigation and was handed a six month suspended sentence and 120 hours of unpaid work.
Superintendent Paul Jeffrey, of West Yorkshire Police, said: “We are pleased that the sentences today reflect the seriousness of the crimes committed by both Kenny and Gorog.
“Their reckless behaviour on the roads of West Yorkshire could have resulted in other members of the public being seriously injured and they also tried to evade arrest by attempting to dispose of evidence.”