Andy Roddick succeeded them at the 21st Century's early dawn and then carried the American flag deep into Grand Slam tournaments for the best part of a decade.
However, no American man has won a Slam title since Roddick won the US Open in 2003. The now-retired Roddick is the only one to have made a Slam final since Agassi made the US Open final in 2005.
But on Monday at the Australian Open a new generation of American male tennis players showed there may be new life in the Stars and Stripes.
World number 62 Ryan Harrison beat Colombia's Santiago Giraldo, lucky loser Tim Smyzcek upset Croatia's Ivo Karlovic, while Brian Baker beat Russia's Alex Bogomolov Jr.
Sam Querrey, the highest ranked American at Melbourne Park after world number 13 John Isner withdrew with a knee injury, also beat Spanish qualifier Daniel Munoz.
But perhaps most encouraging on Monday was the performance of 175th-ranked qualifier Steve Johnson.
Playing his first Australian Open, the 23-year-old from California pushed 10th seed Nicolas Almagro to five sets, and believed that but for two early errors in the decider, could have caused the first upset of the tournament.
"It's definitely frustrating. I thought I had chances to win and a couple of loose points in the fifth set...I think I'd like to take back because they could have changed the momentum of the match," he said.
"I'll definitely be thinking about that for most of the day. He's a great player, he's top-10, but I felt like I was right there with him."
Johnson is comparatively old to be making his first full-time foray onto the main tour, having decided to pursue a collegiate career, and degree in human performance (biomechanics), at the University of Southern California.
The college experience, he added, had prepared his game for the professional level and that a similar career path may be an alternative for aspiring American players.
"John (Isner) really did a lot for my career," Johnson said. "For John to come out after four years of college and be top-10 is big for us (collegiate players).
"I'm hoping to continue that trend (and show) there is a different way rather than turning pro at 14, 15 or 16.
"I think the game is too tough now. You have to be mature ... nobody is winning Grand Slams at 18 any more. It takes people a few more years to figure it out."
In contrast to Johnson, Harrison turned professional at 15 and fashioned an impressive resume as a teenager that included reaching the second round in Houston before his 16th birthday.
Harrison trained with Roddick in Texas during the off-season and considers him something of a mentor, seeking advice on everything from footwork to managing the grind of the tour, and he was more than willing to be a standard bearer for an American resurgence.
"It's a privilege to be thought of like that," the 20-year-old said with a mixture of humility and youthful swagger when asked if he felt he could assume Roddick's mantle.
"To let it motivate you, to drive you to represent not only yourself but your country and family as well.
"The goal of my career is to win Grand Slams and be number one. But every time I have talked about winning Grand Slams and being number one in the world I have always been sure to mention that I know there is a long way to go.
"You have to beat those guys at the top."
Those guys at the top are the four men who have dominated the game for a decade, Roger Federer, Rafa Nadal, Novak Djokovic and Britain's Andy Murray.
Since 2003, only six players other than the four have won a Grand Slam title. Argentina's Juan Martin del Potro is the only active player to have done it when he beat Federer to claim the 2009 US Open.
Johnson, therefore, was quick to point out that it may be unfair to single out American failures at the Grand Slam level.
"As long as there are four guys who are dominating tennis, and nobody else is touching them, then I think (it's unfair to be) putting too much pressure on America not doing well," he said.
"Look at the other countries. Nobody else is winning Slams either. Those guys have won everything for the last 10 years.
"It's tough to say we're behind the times because a lot of people are behind those four guys."