An exhausted Sampras was put on an intravenous drip after failing to convert any of five match points on the way to being being beaten
13-11 in the fifth set of the semi-final, which lasted four hours and 32 minutes.
Korda, who was cramping so badly that he finished the match virtually on one leg, was put to bed, and then put back on the court.
Surely it was expecting too much for the skinny left-hander from the Czech Republic to withstand the force of Stich, who had been irresistible during the previous three weeks in winning the ATP Tour Championship for himself and the Davis Cup for Germany.
The answer came after three hours and 48 minutes yesterday, when Korda fell flat on his face in relief after winning the biggest match of his career, 2-6, 6-4, 7-6, 2-6, 11-9. The cheers of a sporting crowd lifted him to his feet, and the tennis season closed with a crescendo.
Korda said he spent Saturday night dreaming about the Sampras match, and awoke feeling stiff but optimistic. At the back of his mind was the fact that Stich, the defending champion, had also come through a test of endurance, recovering from two sets down in the first semi-final to defeat Stefan Edberg after two hours and 40 minutes.
'Petr deserved it,' Stich said, 'but I think I had more right to be tired than he had, comparing the last four weeks we both had. I mean, he had a tough match, but that happens every tournament. Sometimes he is quite a good actor, and he makes you believe he is tired, and then he is running for every shot. I didn't expect anything else except that he would be as fit as he was today.'
Stich, who had won 31 of his previous 36 matches on German courts, made a confident start, dropping only five points on serve in taking the opening set in 36 minutes.
Signs of tiredness, and the petulance which had punctuated his match with Edberg, were evident when the second set ran away from him. He sulked over line calls and slammed his racket to the court when his shots went astray.
By the end of the fourth set it was anybody's guess which player would have the reserves of physical and mental energy to make the final push for the jackpot. And it was noticeable that while the spectators were eager to lift Stich's spirits, they were also quick to show appreciation of Korda.
Considering the wear and tear of the season, let alone the previous 24 hours, some of the shot-making was breathtaking as both men drove themselves to the corners of the court in search of winners.
Stich was the first to totter in the final set, saving two break points in the second game. Korda then salvaged four break points in the next game, recovering from 0-40. The Czech nearly added to his physical problems in the fourth game, crashing into a ball box beside the umpire's chair while chasing a shot.
The trophy was first within Korda's grasp when he broke for 5-3. Stich, who delivered 30 aces, could also be careless. He hit one of his 14 double-faults on game point. Korda's nerve was then called into question when he was broken to love serving for the match.
Had Stich gone on to win the match, such was his luck with balls which struck the tape on crucial points against both Korda and Edberg that he would have been entitled to dismantle the net and use it to carry away the prize-money.
He clipped the net cord with a second serve when Korda held his first match point at 5-4, and was blessed again when making a volley to save a second in the same game.
It appeared that Stich was about to ride his fortune when Korda's serve was on the point of collapse in the 13th game, but the Czech was able to save four break points, and another at 7-7.
Stich seemed drained after Korda held to love for 10-9, and the German hero was swept away by a cross-court backhand return of a second serve as the Czech converted his third match point.
GRAND SLAM CUP (Munich) Final: P Korda (Cz Rep) bt M Stich (Ger) 2-6 6-4 7-6 2-6 11-9.