A judge described how the teenager was taken out of view of CCTV cameras at Wetherby YOI and subjected to a "frenzy of violence" by Mark Burnett and Daniel Scott.
Burnett was locked up for 15 months and Scott was handed a ten-month sentence after a jury found them both guilty of assault occasioning actual bodily harm.
The court heard the inmate was restrained after assaulting one of the defendants' colleagues.
15-year-old inmate's neck slashed at Wetherby YOIHe was taken into a corridor before Burnett said to him: "Do you think it's funny to assault a prison officer?"
Burnett then delivered a series of punches and upper cuts to the teenager's face as his arms were held.
Scott joined in the attack and threw punches.
The violence ended when other prison officers went to protect the inmate.
Recorder Ben Nolan, QC, told the pair: "This was an assault in the course of your duties as prison officers.
"It was a gross dereliction of those duties. He was 17. In law, he was a child in your care."
Recorder Nolan described the assault as a "frenzy of violence" that was "downright brutal."
He said: "It was not only a breach of trust and a breach of power, but it undermines the work of the prison service.
"The integrity of the prison estate requires discipline."
The trial at Leeds Crown Court heard Burnett, 51, and Scott, 28, approached their colleagues after the attack, December 7, 2016, and said "they should get their stories straight".
The defendants denied the offence at trial, claiming the inmate had suffered the injuries when he was initially restrained.
Recorder Nolan described their defence cases as "pathetic".
He praised the prison officers who gave evidence against the two men.
Lawyers for the two men asked Recorder Nolan to consider suspending the prison sentences.
Patricia Doherty, for Burnett, said he was in a position to pay compensation to the victim.
Robin Freize, for Scott, said: "This appears to be a one-off and he was not somebody who had difficulty controlling his temper."
After the case, Detective Inspector David Roberts, who heads the Leeds District Prison Investigation Team, said:
“As prison officers, Burnett and Scott were responsible for the security and the safety of young offenders at Wetherby, but they abused their positions of trust to attack a 17-year-old prisoner while he was being restrained after assaulting one of their colleagues.
“The evidence showed the victim was repeatedly punched in the face by both men causing significant visible injuries.
“This incident was the subject of a thorough and comprehensive investigation by detectives from the Leeds District Prison Investigation Team which has resulted in both men being convicted and sentenced.
“At the heart of the prosecution case was the evidence provided by other prison officers who were understandably appalled at these men’s actions and at their attempts to cover up what they had done.
“Any kind of violence in prisons is just as unacceptable as it is in society and we work closely with the prison authorities to investigate incidents and bring offenders to justice.
“Where that violence is committed by those in positions of responsibility it rightly attracts an even greater focus.
“No-one is above the law and anyone who misuses their authority to commit offences against those in their care should expect to pay the price, as these men have done.”
INMATE 'GURGLING' AND SPITTING BLOOD AFTER A BEING RESTRAINED AND REPEATEDLY PUNCHED IN FACE BY OFFICERS
Jurors heard the 17-year-old inmate was "gurgling" and spitting blood after being attack by prison officers Mark Burnett and Daniel Scott.
A healthcare nurse at Wetherby YOI was left "shocked and upset" when she saw his injuries.
The incident took place around 4.30pm on December 7, 2016, after the inmate attacked another prison officer
The teenager was taken to the ground and restrained by a number of officers, including Burnett and Scott.
He was then taken into a corridor known as the control and restraint stairwell.
Katy Rafter, prosecuting, said Burnett locked an exterior door to the prison yard.
She said there was "no operational reason" for closing the door and it meant they could not been seen by cameras.
The prosecutor said: "(The inmate) was punched to the face by Burnett and his head was pushed down by Scott.
"He was subjected to multiple punches to the face by both defendants.
"(The inmate) was unable to defend himself and was scared.
"He soon began spitting blood and began to feel his face swell up.
"He was inside the corridor for exactly a minute."
The door to the corridor was forced open by an officer who went to protect the inmate.
He said to Burnett: "What the **** are you doing?"
The court heard the officers kept the inmate bent over as they walked him through the prison yard so that his injuries were not visible to others.
The healthcare nurse was so concerned about what she was seeing that she asked them to stop so she could check the inmate's injuries.
Miss Rafter said: "Burnett told them to leave them so they could do their jobs."
"The nurse was shocked and upset when she saw the injuries."
The jury heard the inmate was later stripped and given fresh clothing.
Miss Rafter said: "The prosecution say that was an attempt to hide the extent of his injuries."
He was assessed by the nurse who said he needed immediate hospital treatment.
Miss Rafter said Burnett later approached a prison officer who had been standing outside the door when the attack happened and said to him: "How are we going to get out of this?"
The officer replied to Burnett that he had played no part in the incident.
Both defendants approached another officer the following day ahead of a debriefing and said they "should get their stories straight."
That officer was initially too scared to give a true account of the incident.
A week later the officer spoke to another colleague and they agreed to go to the governor and give a true account of the attack.
Burnett and Scott were interviewed and claimed the inmate must have suffered his injuries as he was restrained after attacking officer Harper.
Miss Rafter said: "The prosecution case is that they exacted their own retribution on behalf of their colleague who was assaulted and tried to lie and cover up what happened."
Both defendants appeared shocked in the dock as the jury returned unanimous verdicts.