Mohammed Fike Butt today pleaded guilty to murdering Jason Llanwarne midway through his trial at Leeds Crown Court.
The 31-year-old defendant was also accused of the attempted murder of Dean Ward and Scott Chalders during the same incident on North Lane on September 14 last year.
Butt entered guilty pleas to the lesser charges of attempting to cause grievous bodily harm with intent.
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The pleas were accepted by the Crown Prosecution Service and Butt will be sentenced at 10am on Wednesday (March 31).
During the trial, jurors heard how Butt laughed as he drove his car over Mr Llanwarne's body as he lay prone on the pavement after being deliberately knocked down.
Butt then went to a takeaway and ordered himself a portion of cheesy chips moments after causing the fatal injuries.
Prosecutors said Butt carried out the attack to teach the three men "a lesson" during a dispute over drugs.
The court was shown CCTV footage of Butt getting into his car after a fight with the men on North Lane.
Footage of the attack in which Butt used his car "as a weapon" was played in court.
Prosecutor Stephen Wood QC described how Butt first drove his car at Mr Chalders and Mr Ward, causing injuries to Mr Chalder's leg.
The defendant's Mazda then re-joined the carriageway before turning around, mounting the pavement again and driving at all three men.
Mr Llanwarne was struck and carried on the bonnet before falling to the floor.
Butt then turned the vehicle around and drove at the men a third time despite his windscreen being smashed.
Mr Wood said a wheel was deliberately driven over Mr Llanwarne while his friends were trying to pull his limp body out of the way.
Butt, of Cross Flatts Avenue, Beeston, abandoned his car behind a nearby takeaway and called a taxi.
Mr Wood said: "He went into Dino's takeaway where - you may think seemingly unconcerned by what occurred - he bought himself some cheesy chips."
The incident happened shortly before 10.30pm.
Mr Wood said Llanwarne had been in contact with Butt earlier in the evening to arrange to buy drugs from him.
Jurors were told Mr Llanwarne and his two friends were drug users.
CCTV footage from the area showed Mr Llanwarne getting into the Mazda with Butt and an unknown male.
Mr Wood said: "It seems. . .a dispute erupted while Jason was inside the car.
Moments later, Butt and the other male were captured on the footage fighting with Mr Llanwarne in the street.
Mr Llanwarne was punched hard in the face by Butt and knocked to the floor.
Mr Ward and Mr Chalders then ran to help their friend.
Butt went to his car and drove at the men seconds later.
Mr Llanwarne suffered multiple injuries to his head and body and was declared dead at Leeds General Infirmary.
A pathologist said his death was caused by a tear to an artery in his neck.