'Hopefully we'll win this thing for the next eight or nine years,' Courier said after his 6-3, 3-6, 6-3, 6-4 triumph secured a 3-1 win over Switzerland in the final at Fort Worth, Texas, on Sunday.
Courier, despite winning the Australian and French Opens in the first half of the year, had an alarming dip in fortunes during the rest of the season and his previous record in the Davis Cup was not as convincing as his world ranking would suggest.
His fragility was underlined when he was defeated by Marc Rosset on the first day of the final but his determination enabled him to see off the challenge of Hlasek - who at one stage had break points for a 3-0 lead in the third set - in the crucial rubber.
'There's nothing like winning for a team and whenever I'm needed to play, I'll be there,' Courier said.
Victory was equally sweet for his team-mate Pete Sampras, the 21-year-old world No 3. His Davis Cup debut in last year's final was a personal nightmare as he lost both of his singles matches.
'It feels great for me personally after last year,' said Sampras, who in tandem with John McEnroe, fought back to win the doubles after trailing by two sets to love against Hlasek and Rosset.
The fourth member of the US team, the Wimbledon champion Andre Agassi, did not need to play his final match but had set the Americans on their way with an impressive opening victory against Hlasek.
'It was a great experience for all of us to be part of such a strong team,' Agassi said. 'There's a lot of support for each other. I think there is a strong motivation to keep this team together.'
Tom Gorman, the US captain, paid tribute to the Swiss. 'They did themselves proud,' he said, 'but having a two-man team finally caught up with them.'
Rosset and Hlasek, the 35th and 36th ranked players in the world, did appear to tire in the doubles and playing three days in a row also took its toll on Hlasek on Sunday.
'I have the utmost respect for both those guys,' Courier said. 'They're both class acts.'
DAVIS CUP FINAL (Fort Worth, Texas): United States beat Switzerland 3-1 (US names first): A Agassi bt J Hlasek 6-1 6-2 6-2; J Courier lost to M Rosset 6-3 6-7 3-6 6-4 6-4; J McEnroe and P Sampras bt Hlasek and Rosset 6-7 6-7 7-5 6-1 6-2; Courier bt Hlasek 6-3 3-6 6-3 6-4.Reuse content