Tyrelle Harris, from West Bromwich, was last month given a life sentence with a minimum 20-year term for stabbing Karl Gallagher to death outside a Smethwick shopping centre last year.
And now he has been given a separate 10-month sentence for leading police on a high-speed chase through the Black Country 20 months before he committed murder.
However the judge at Wolverhampton Crown Court ordered the term be served concurrently with the murder sentence, meaning Harris will not spend any longer in prison.
The teenage killer, now aged 20, had pleaded guilty to a charge of dangerous driving at an earlier hearing connected with the incident in August 2018 when he was 17.
Prosecutor Howard Searle told the court on Monday how Harris initially got away from police after they tried to block the Renault Clio he was driving in at around 10.45pm on August 25, 2018.
Mr Searle said: "The pursuit took place over 10 minutes in and around the West Bromwich and Tipton areas. It started off as an attempt by police to block in the vehicle but he moved around them onto a public pavement, clipping a lamppost in the process causing damage to the vehicle.
"The vehicle was pursued for around 10 minutes in residential streets reaching speeds of up to 70mph in a 30mph zone.
"Aggravating factors include on three occasions the defendant drove around a roundabout in an incorrect manner and he drove up a dual carriageway facing oncoming traffic. It was an extremely dangerous piece of dangerous driving."
The vehicle eventually came to a stop near a public house before Harris was arrested a short distance away.
Sunit Sandhu, defending, added nothing further during the short hearing.
Judge Michael Chambers QC told Harris: "This was a high-speed pursuit away from police officers which was highly dangerous – roundabouts, the wrong way along a carriageway.
"Taking into account the sort of sentence had you been sentenced when you were 17 and also reducing it by a third to fact your guilty plea. It will be a sentence of 10 months in a young offenders institute.
"You are currently serving a long sentence for murder. I don't propose to make the 10-month sentence consecutive, so it will be served concurrently. I am also required to disqualify you from driving for 12 months and you will be required to take an extended driving test."
The same judge sentenced Harris, formerly of Helvellyn Way, West Bromwich, to spend at least 20 years after he was convicted of murder in March having knifed 31-year-old Mr Gallagher at West Cross Shopping Centre.
Mobile phone footage, which was widely shared on social media, captured the moment Mr Gallagher was stabbed in the chest before he collapsed onto the floor seconds later.