The scouts from Doncaster and Sheffield rushed to help, after hearing the stricken walker's cries, while they were taking part in a challenge on Kinder Scout. He had been struck by a runaway boulder on the slope at Grindsbrook Clough.
Using their training, the teenagers from Tickhill-based Phoenix Explorer Scouts and Woodseats Venture Unit gave first aid, kept him warm and raised the alarm.
The walker, a 19-year-old Sheffield Hallam University student, who has not been named, is recovering in the Northern General Hospital after the incident on Saturday. Both bones in his lower right leg were broken.
Ben Nuttall, aged 17, from the Woodseats group, said he and teammates Andrew Batley, 17, Andrew Taylor, 17 and Louis Sheeron, 16, were on the last stage of the trek when they heard shouting.
They were joined at the scene, on the way down from the summit of Kinder Scout to Edale, by three members of Tickhill Phoenix group.
Jo Taylor, 16, stayed with the Sheffield team at the scene, while Mark Harrop and Adam Walker, also 16, went to find help.
Mark said: "There was no phone reception so we walked to the top of the clough, where we got a signal and alerted Mountain Rescue."
Ben said: "We saw the man lying in a gully with his friend and were told he had a broken leg. Andrew Taylor and I are trained lifeguards and we all have general first-aid qualifications, so we knew what to do.
"We sorted him out, got him into some warm clothes and put a survival blanket round him and checked his leg out. His ankle was quite bruised, so we carefully removed his shoe and sock, and gave him another sock.
"He was in shock, and shaking quite badly, so we ensured he was warm enough and gave him some chocolate to ensure he had sugar inside him."
The teams discovered the man at about 5pm, and although Edale Mountain Rescue arrived within 30 minutes, it was not until 10.30pm they managed to bring him down to safety.
James Stubley, deputy leader of Edale Mountain Rescue, said: "We had requested an RAF helicopter but it was windy and there was low cloud so it was unable to reach the scene.
"We had carry the man down to Edale, where he was taken to the Northern General Hospital by ambulance."
Mr Stubley added: "Grindsbrook Clough is one of the main routes but at that time there are only limited numbers of people coming back down and there was a danger of hypothermia.
"It was fortunate those couple of groups of scouts heard him shouting, otherwise his rescue could have taken longer as his friend would have had to seek help.
"The scouts handled things very well, keeping him warm and giving an accurate location so we knew where to reach him."
It was the first time the scouts had put their first aid training into practice.
The rescue happened during the Apex Challenge, entered by 150 scouts aged from 14 to 25 from across the UK.
They spent two days in the Peak District tackling tough challenges such as climbing, abseiling and canoeing, while also battling for points.
Graham Hunt, leader of Phoenix Explorers, said: "I can't give them enough praise, they did a fantastic job. All the skills they have picked up during their scouting career really paid off."
Event Organiser Matt Richards said: "This mountain rescue incident just summed up the spirit of the event. Despite the young people racing against the clock to complete their challenges, they didn't hesitate to stop and help this member of the public who clearly needed assistance.
"It's great that we were able to do our bit to help and it showed the value of the training they've been given during their time in scouting. These teenagers can be very proud of what they did."

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