A court was shown footage of the incident in which the schoolboy took the weapon out of a bag and attacked him in an aisle at Premier Stores on Harehills Lane.
Leeds Crown Court heard how the boy and three others, two aged 16 and one aged 18, targeted the victim as revenge during a series of violent incidents between rival teen gangs.
Frances Pencheon, prosecuting, said the four defendants travelled to the store by taxi in the early hours of October 12 last year.
One of them was heard to shout "let's bang him" before they carried out the violence.
One of the 16-year-olds went up to the victim and began punching him repeatedly.
The other 16-year-old picked up a bottle from a shelf and struck him a number of times.
The 14-year-old then cornered the boy and struck him twice with the machete.
The fourth member of the group, Tye Jeffers, then aged 18, appeared to squirt liquid at the victim and blocked his escape from the shop.
The prosecutor said the victim managed to run home after the attack and told his mum he had been stabbed.
His coat had been ripped by the machete blade.
When the coat was removed he was covered in blood and had a deep wound to his back.
The teenager's mum rang an ambulance while her partner applied pressure to the wound until paramedics arrived.
Ms Pencheon said the victim suffered a 15cm wound to his back which cut through fat and muscle tissue, causing a fracture to his rib.
He had to undergo surgery to have the wound cleansed and closed.
The court heard the youngster has been left scarred for life.
The four defendants were arrested at a property in Leeds on October 19.
Police recovered three machetes when they searched the property.
One of the machetes was similar to the weapon the 14-year-old had been holding in the footage of the attack.
Three of the defendants cannot be named due to their age.
The 14-year-old pleaded guilty to wounding with intent.
He was made the subject of a two-year youth rehabilitation order when he appeared before the court at a hearing last week.
Jeffers, now aged 19, and the two other defendants pleaded guilty to affray and were sentenced today (March 14).
Jeffers, of Kitchener Street, Harehills, was made the subject of a 12-month community order during which he must complete 20 rehabilitation activity requirement days and complete 120 hours of unpaid work.
Craig Sutcliffe, mitigating for Jeffers, said the defendant had been in custody since being arrested.
Mr Sutcliffe said Jeffers has a partner and a young child and was determined not to re-offend.
The barrister said: "There is a real prospect of rehabilitation."
Judge Penelope Belcher told Jeffers: "You are the oldest of this group. In law, at least, you are an adult. But you were far from behaving like one."
The 16-year-old defendant was made the subject of a two-year youth rehabilitation order.
The fourth defendant, who is now aged 17, was made the subject of a youth rehabilitation order for two years.
He was also made the subject of an electronically-tagged prohibited activity requirement which bans him from entering any area with an LS postcode for three months.
Judge Belcher said: "It is clear that there have been prior incidents between gangs of youths.
"Taking retribution into your own hands is criminal and that is why you are before the courts.
"If everyone went around dishing out revenge there would be no law and order.
"There would be utter chaos and everybody would be at risk of being injured by those carrying weapons
"(The victim) is not prepared to make a complaint against you. Maybe through fear of retribution.
"But the CCTV footage caught this thoroughly horrible incident."
"You are very fortunate that none of you are before this court on a manslaughter or a murder charge.
"If you were there would be no alternatives to custody."