Corporal Mike French, 34, was taking part in a jump at Whitehaven Air Show in Cumbria on Friday night when he got into difficulty.
Quick-thinking Corporal Wayne Shorthouse, 32, swooped over to catch his struggling teammate before bringing him in to land safely in the water at Queens Dock.
Thousands of anxious onlookers watched the stricken parachutist “violently kicking” while tangled up in his parachute.
An army spokesman said it was the first time a parachute had failed in 25 years and that they were investigating to find out the cause of the incident.
Cpl French said the drama unfolded while they were stacking their canopies in formation. Cpl Shorthouse was on the top and he dangled beneath the tangled canopies.
He said: “This situation is something we prepare ourselves for in our vigorous training, and so I was able to give instructions to Wayne above so that he could pilot us safely into the drop zone, which in this case was the harbour.
“Though this is the first time this has happened on a public display, it has happened before in training, and so we were well prepared for it and didn’t feel as though we were in any danger. We reacted as a team and that is what got us out of what was a potentially dangerous situation.”
Cpl French said he owed his colleague “a pint of beer maybe” for helping him out because “my parachute wasn’t too clever”.
“It is all part of being in the skydiving world. It is a very dangerous sport. Display parachuting, and especially canopy formations within display parachuting, is a very difficult aspect of skydiving. Constantly training is one of the things that kept us safe, and the communication,” he added.
Cpl Shorthouse, of Plymouth, said he was “just doing his job” .
He said: “When something like this happens, the training just kicks in. The time spent practising the drills pays off in situations like this. You instinctively know what to do.
“I’m glad I was able to help my teammate out, but we are all trained to be able to deal with emergency situations like this.”
French joined the Red Devils in 2010. Apart from being part of the flying parachutes squad, he organises all the team’s tandem days, when the public are able to skydive with the Red Devils.
Shorthouse, who began his service with 3 Para in 2001, has completed tours in Northern Ireland, two tours of Iraq and three tours of Afghanistan.
Onlooker Lucy Milne said: “He was violently kicking his legs and he was trying to get free or trying to manoeuvre. Above him was another man tangled up in his parachute. His parachute was collapsed. They started picking up speed and he was wiggling his legs even more.”
Everyone clapped when they both popped up in the water and there was a “big sigh of relief that they were both safe”, Milne said. A rescue boat picked them up and one of them gave a wave to show he was safe, she added.
Milne said: “He was so frantically kicking his legs that there was something seriously wrong. It was amazing how he managed to get into the water and not hurt himself or the man above him.”
Volunteer Dianne Richardson said it appeared the chutes did open, but that it was as they were manoeuvring into the stack position that something happened.
“To be honest, everybody thought they had been tangled up, but it was only afterwards that they found out that one of the guys managed to manoeuvre to safety,” she said.
The Red Devils were formed in 1963 and carry out more than 60 displays every year.
The team comprises 12 soldiers from the three battalions of the Parachute Regiment, who all have at least three years’ experience.
A message was later posted on the show’s Facebook page, saying: “We can confirm that the Red Devil parachutists are both safe and sound.
“Our safety procedures worked perfectly.”