Pella came into the match with little in the way of form since the French Open, but performed above his recent level to win by virtue of being more consistent than the British No 2.
Dan Evans, who narrowly missed out on playing despite being at home on indoor courts, will have been looking on in frustration after Edmund unravelled from a position of strength.
He had the bigger weapons and led 3-2 with a break in the third but then played a horrendous service game that seemed to blow a hole in his confidence. Edmund was too trigger happy on his forehand, but as the youngest player on either side it was a lot to expect him to come to the rescue against a more experienced opponent.
Murray had been left shattered after his longest ever match proved all for nothing as he dramatically lost his proud record of never having been defeated in a home Davis Cup singles.
The world No 2 was driven to physical exhaustion as, on the day of his grandfather's funeral, he was downed by a magnificent effort from Juan Martin Del Potro.
This time, unlike in the Olympic final, Murray could not resist the resurgent Argentinian, who fought back to win 6-4 5-7 6-7 6-3 6-4 in five hours and seven minutes.
That was 13 minutes longer than Murray's epic against Kei Nishikori in March's first round at Birmingham, and spells the end of the twenty-match streak which has seen him always win at singles on home turf.
'It was fine margins,' said a terse and plainly wounded Murray afterwards. 'It could have gone either way but he played a little bit better in the fifth set. Both of us were tired at the end.'
The plan has been for Murray to come back and play doubles today with brother Jamie, and he is sure to feel it in his body.
'I've never played a match this long so I will have to see how I wake up and make a decision then,' said Murray, who said that the death of his grandfather had made it a difficult build-up to the match.
'It has been hard but I always planned on playing. I'm very proud of how I fought, I tried as best as I could.'
Towards the end he had a verbal exchange with boisterous Argentinian fans but played that down: 'I just said keep the noise down between first and second serves. I thought the crowd were fair on both sides.'
Murray served 35 aces but even that was not enough to stop Del Potro, making a mockery of his falsely depressed ranking of 64, coming back to put the visitors ahead.
The 29 year-old Scot, before his adoring fans, looked to have done the hard work when he took the third set tiebreak 7-5. With his history of wrist problems it was 2010 since the 6' 6' giant from Tandil had won a full five setter.
But Murray's concentration dipped in the fourth, and in the draining decider he was second best, broken at 3-3 when his opponent ripped a glorious running forehand pass down the line.
The Scot battled to the end but has played more matches than anyone on tour this summer. That, plus the emotion of the past week, may have sapped him of a crucial few percentage points.
This should not detract from the performance of Del Potro, who just looks better and better since overcoming the career-threatening wrist surgeries to his wrist.
While his forehand was as potent as ever, it was his serve that was excellent for long periods and he made only 28 unforced errors across the five sets.
After the now customary rendition of 'The Banks of Loch Lomond' Murray began well enough, breaking straightaway for 2-0 with the use of three exquisite lobs.
Yet there were early danger signs in the sheer consistency of Del Potro, who broke back immediately and went on a run of four games without losing a single point when serving.
With the 100 or so Argentinian fans at the Emirates Arena making their presence known, the 29 year-old Scot changed his tactics somewhat to attack the net and be more adventurous against the metronomic but unthreatening Del Potro backhand.
The world No 2 winning the third set will go down as one of his gutsiest sets in Davis Cup play. Dredging up his mental and physical resources he twice came back from a break down eventually clinch it 7-5 in a tiebreak which had looked beyond his reach.
But in a pivotal game he saved a set point with an exquisite forehand lob and got back on even terms with his third break point.
In the tiebreak two aces carried him to 4-1, but groundstroke errors took it back to 5-5. With the crowd's excitement and anxiety at fever pitch Murray created set point with a smash, and then delivered a first serve winner to the backhand.
Given that Del Potro had lost his previous seven matches that have gone to five sets that looked to be the decisive blow.
But the mental effort of getting ahead appeared to have taken its toll on Murray, and an error-strewn game saw the Argentinian break for 3-1. This time the world number two could not turn it around and the fifth set war of attrition arrived with more than four hours already on the clock.
In the other semi-final Croatia and France are tied at 1-1, but that looks unlikely to be relevant to GB.
