The 21-year-old from Beverley was given the responsibility of being Britain’s No 1 player in only his second tie after Murray pulled out.
Edmund secured his first win in the competition in impressive fashion against Janko Tipsarevic on Friday and, after Jamie Murray and Dom Inglot put Britain 2-1 up in Belgrade on Saturday, found himself in the position of trying to win the tie.
He played superbly against his fellow stand-in No 1 Dusan Lajovic, overcoming a wobble with the finish line in sight to win 6-3 6-4 7-6 (7/5).
The victory extended Britain’s winning run in the competition to six ties and set up a semi-final against Argentina in September, probably in Glasgow.
Andy Murray is very likely to return for that one, making Britain firm favourites to reach the final once again.
Edmund said: “It’s definitely a very proud moment. Friday was a really nice thing to do. I was really pleased with that.
“But it’s one thing winning and then losing the other one. To win twice feels good away from home, so I’m very proud. I’ve been at a lot of ties, on the bench, hitting. It’s nice to feel like I did it for the team.
“Growing up you watch tennis and you think of these moments, what it would be like to win for Great Britain and it’s nice to be able to do that.”
Britain had not won a tie at World Group level without Andy Murray since 1986 and to do so away from home on clay, albeit against a Serbia team missing Novak Djokovic and Viktor Troicki, was another hugely impressive achievement for Leon Smith’s men.
And to know they now have a player besides Murray who could potentially win plenty more singles rubbers at this level is also highly significant.
Smith heaped praise on Edmund, saying: “He’s worked really, really hard to get to this stage.
“I’m just immensely proud, but he should be really proud of himself and the team that works with him as well because he’s improved so much physically.
“A lot of his game has improved so much. His backhand is rock solid now, serve is getting better all the time and his forehand is just so huge. It’s such a great shot.
“And the good thing for Kyle, he won’t mind me saying that, is there’s a whole heap of stuff that he’s going to get better at. That’s why I think he’s just going to keep kicking on and every year he’s just going to get better and better.”
Andy Murray may not have played in the tie but his remarkable effort in travelling to Belgrade to support the team undoubtedly made a difference.
It was a rather different Sunday for the world No 2, who seven days after that glorious day at the All England Club found himself sitting in conditions more typical of a Scottish summer.
But persistent drizzle did not prevent the match starting on time and Edmund, ranked 14 places above Lajovic at 67 in the world, immediately took control.
Lajovic is a solid player and a very good mover on clay but the 26-year-old does not have a shot to rival Edmund’s forehand – he hit 27 winners off that wing alone.
The 21-year-old dominated the first two sets, holding his nerve in the second in the face of growing Serbian crowd support, and looked poised for victory serving at 5-4 in the third.
Edmund had only faced one break point in the whole match but his first serve deserted him and he tightened up on his forehand as Lajovic levelled.
The Serbian then had two chances to take it to a fourth set but Edmund saved them both and recovered from 4-2 down in the tie-break with some big forehands.
On his first match point, Lajovic drove a backhand wide, and Edmund collapsed to the clay in celebration before being embraced by his team-mates.
“I went a little bit passive, just ever so slightly, serving for it, I learned from that so I thought don’t make that same mistake again,” said Edmund.
“The last point was pressure on him, match point down, two sets down.
“He’s got to hold serve. There’s pressure both sides but I stayed tough when I needed to be,” he added.
Meanwhile, British No 4 Dan Evans has turned down the chance to represent Britain at the Olympics.
The 26-year-old was the next in line following Tomas Berdych’s withdrawal on Saturday but, given the late notice and the lack of ranking points on offer, has opted to stick to his planned schedule.