Hewitt and Agassi posted round-robin victories in the first day of action at the $3.65 million Tennis Masters Cup, the final ATP tournament of the season.
The second-seed and the U.S. Open champion, Hewitt woked up after a sluggish first set to handle No. 7 Sebastien Grosjean of France, 3-6, 6-2, 6-3, to move just 28 points behind top-seeded Gustavo Kuerten of Brazil in the ATP Tour Champions Race 2001 standings.
The third-seeded Agassi needed just 73 minutes to dispatch No. 6 Patrick Rafter of Australia, 6-2, 6-4.
A semifinalist at the Australian and French Opens, Grosjean needed to capture the Tennis Masters Series event in Paris two weeks ago to qualify for this tournament for the first time, and showed the same winning form when he broke in the match's fourth game and won the first set.
Hewitt rallied in the second set, taking a 4-1 lead and breaking his foe's serve to level the match. The 20-year-old from Adelaide snatched Grosjean's first serve of the third set and soon owned a 4-1 advantage.
Hewitt served out the victory to improve to 4-2 lifetime against Grosjean, also defeating the Frenchman in Sydney in January en route to his second straight adidas International title.
"As soon as it got into the third set it was a dogfight. It's nice to get through the first match," Hewitt said. "I was also able to get onto his serve a little better in the second and third sets and I think that's what did it."
"He picked up his game in the second set and maybe I got a little tired," Grosjean said. "You know the big week in Paris and then the journey - maybe it left me a little flat."
Hewitt and Grosjean will meet again in Melbourne in three weeks in the Davis Cup final.
Agassi, the Australian Open champion, fell behind Rafter, 0-2, before taking six straight games. Rafter double faulted at 4-4 of the second set and Agassi held on to snap a three-match losing streak.
This was Agassi's first win since reaching the quarterfinals of the U.S. Open in early September, and his 10th in 15 meetings with Rafter.
The eight players to qualify for this elite season-ending event are split into two groups, named after Australian tennis legends John Newcombe and Ken Rosewall. Each player participates in three matches, with the two leading players from each group advancing to the elimination semifinals. The winner of the semifinals square off in a best-of-five set final.
Monday's action featured the Newcombe Group. The Rosewall Group takes to the court on Tuesday as Kuerten, the top seed and defending champion, faces No. 8 Ivanisevic and fourth seed Juan Carlos Ferrero of Spain takes on fifth seed and 1997 finalist Yevgeny Kafelnikov of Russia.
Trying to become the youngest player to finish the year ranked No. 1, Hewitt won his first career Grand Slam title in New York in September and claimed four other crowns.
Agassi, a winner of four titles this year, hopes to become the first player older than 30 to take over the top spot in the rankings. He has appeared in the final of this event the last two years but has never won the season-ending tournament in three tries in the championship match.
Rafter was playing for the first time in more than a month. He has said he will retire after Australia plays France in Davis Cup final in Melbourne in three weeks.
If the champion wins all of his matches, then he departs with $1.52 million. Otherwise, he earns $700,000.
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UPI Sports Results for September 20, 2014