Sampras took away Becker's title with a 3-6, 7-6, 7-6, 6-7, 6-4 victory, surviving 32 aces in the match that lasted four hours.
Becker, 29, played superbly, enjoyed the raucous support of 15,000 fans and saved two match points in the fourth set but the American matched him shot for shot and won the key points.
Sampras' victory in an event that brought together the top eight players in the world also avenged defeats by Becker in their two previous matches, the last three days ago in a round-robin match.
The outcome was a repeat of the 1994 championship, when Becker also beat Sampras in the round-robin stage, only to lose the final.
It was one the biggest pay days in tennis, with Sampras collecting $1.34m (pounds 830,000) and Becker having to settle for $640,000.
The German began the match by rifling four straight aces and he served with astonishing consistency. Sampras suffered a break in the fourth game, when Becker hit some superb returns. He finished off the set with a backhand winner.
Becker was forced to save two break points in the sixth game of the second set before Sampras finished off the first tie-break with a volley.
Sampras had some problems in the sixth game of the third set but got out of trouble with two aces to save two break points. In the second tie- break, Becker came back from a 3-0 deficit, but served a double fault to go 5-4 down with Sampras to serve. A service winner and a backhand passing shot clinched the set for Sampras.
Three spectacular returns gave Becker two break points in the opening game of the fourth. But again Sampras shrugged them off, hitting winning volleys behind good serves.
Sampras came within two points of winning the match at 5-4 in the fourth, but this time it was Becker who responded to adversity, hitting a service winner, a volley and an ace.
The tie-break produced a thriller. Sampras had two match points, but wasted the first with a long backhand and then the next with a long forehand. Becker then squandered four set points, but converted the fifth when Sampras hit a forehand volley long.
Becker held his serve throughout his 27 service games, facing only two break points, but he finally cracked in the 28th to trail 5-4 in the fifth set.
The German saved two break points, but Sampras converted the third with a brilliant backhand passing shot.
Serving for the title, Sampras wasted two more match points, but clinched the match when Becker netted a backhand after a long rally from the baseline.
The two rivals hugged warmly at the net. "I don't think so," Sampras replied when asked if he had ever played a more dramatic match. "That was the best match of my life. I am very proud of it. I tried my best, but it was not to be," Becker said.Reuse content