The victory gave the United States an insurmountable 3-1 lead in the best-of-five series and their Davis Cup title. It was only the third victory in eight Davis Cup matches for Courier, the first American since John McEnroe in 1984 to finish the year as the No 1 player in the world.
Hlasek dominated the second set by attacking the net. But Hlasek was deflated after squandering four game points in the eighth game of the third set before being broken. Courier then won his serve to love to take the set.
'That was decisive,' he said, admitting: 'It was a bit of a struggle early on and I was not moving very well.' Courier said his team- mate, Andre Agassi, had helped him through the early crisis by urging him to 'loosen up'.
After a 10-minute intermission, both players held serve until the seventh game of the fourth set when Hlasek hit an easy overhead wide on game point. Courier won the next two points to convert the break and take a 4-3 lead.
After both players held serve in the eighth and ninth games, Courier watched Hlasek's forehand return of serve float long on match point, and his team-mates rushed on to the court and hoisted him on to their shoulders.
Hlasek and Marc Rosset, who teamed up to win three tournaments in 1992, including the French Open, had taken the first two sets before faltering to the fresher US doubles team of McEnroe and Pete Sampras on Saturday.
It represented the best American comeback in Davis Cup doubles since 1958 and demoralised the fatigued Swiss team nearing the brink of an historic upset in their first Davis Cup final.
McEnroe finally launched the counter-attack with a fierce service return that broke Rosset and gave the United States the third set of the doubles.
In the 10-minute intermission after that set, he made sure the momentum stayed with the Americans. 'He was in the locker-room, pumped up, ranting and raving,' Sampras said. 'He was getting pumped up, 'Let's kick some ass'. He was on that roll.'
He and Sampras did precisely that in the last two sets, Sampras finally finding his range with his forehand and McEnroe delivering some devastating serves.
DAVIS CUP FINAL (Fort Worth, Texas) Friday: Singles: A Agassi (US) bt J Hlasek (Swit) 6-1 6-2 6-2; M Rosset (Swit) bt J Courier (US) 6-3 6-7
3-6 6-4 6-4. Saturday: Doubles: J McEnroe and P Sampras bt Hlasek and Rosset 6-7 6-7 7-5 6-1 6-2. Yesterday: Courier bt Hlasek 6-3 3-6 6-3 6-4.
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