Marek Stasiak and Harvey Stokeld were caught on camera attacking the victim as he was on the ground during the disturbance in Roundhay.
Leeds Crown Court heard the incident happened after the pair had spent the evening drinking.
Alasdair Campbell, prosecuting, said the incident took place in the early hours of August 23, 2020.
The victim had been out socialising with friends when they went into Domino's, on Street Lane, and were waiting for food.
Stasiak and Stokeld went into the pizza takeaway with another group a short time later.
Mr Campbell said the two groups engaged in conversation and were initially friendly towards each other.
They began walking towards the main road together after leaving the takeaway and the conversation continued to be amicable.
There was then a confrontation between the victim and one of the defendants' friends.
CCTV footage showed the two groups in front of Domino's and the victim backing away.
Mr Campbell said the victim was the first to make contact with the defendants.
He was followed by Stasiak as he turned away.
Stasiak punched him to the side of the head and he fell to the ground.
Stokeld joined in and kicked the man to the upper body or head area.
Stasiak then appeared to stamp or kick him as he was on the ground but it was not clear where the blow landed.
The victim suffered a fracture to his cheekbone.
Both men were arrested and Stasiak said during an interview that he had acted in self defence.
Stokeld said the victim had been aggressive and tried to fight with his friend.
He accepted that his own actions were aggressive and was remorseful for what he had done.
Stasiak, 21, of Talbot Avenue, Moor Allerton, and Stokeld, 22, of Parkside Road, Meanwood, pleaded guilty to inflicting grievous bodily harm.
Kara Frith, for Stasiak, said the defendant admitted the offence at an early stage.
Ms Frith said her client worked as an air conditioning engineer, adding:"He is respectful and hard working and highly respected by his colleagues".
Michael Devlin, for Stokeld, said the defendant also pleaded guilty to the offence at an early stage and had not been in trouble in 17 months since the incident.
Both defendants were given prison sentences of 18 months, suspended for two years.
They were also made the subject of a curfew, between 7pm and 5am daily, for six months.
The pair were also ordered to pay fines and costs totalling £756.
Judge Tom Bayliss QC said: "It was a cowardly attack in which you kicked him in the head.
"This was an offence committed at night when you were no doubt in drink.
"I can put a stop to that for six months.
"Your activities will be curtailed until July when you will be allowed out again".