Gumy has worked with Argentines Guillermo Canas and Guillermo Coria, as well as Brazilian Kuerten.
Kuerten broke Agassi twice to win the second set, and served two games to love.
Kuerten fought back, surviving two match points and seven deuces to hold serve and trail 5-4.
Federer will next meet Gustavo Kuerten, who beat Goran Ivanisevic 6-2 6-4 to reach the second round.
Kuerten hit 20 winners to Ivanisevic's 11 and made just 15 unforced errors to his opponent's 24.
Gaudio awaits the winner of Wednesday's second quarter-final between fellow Argentine David Nalbandian and Brazil's Gustavo Kuerten.
However, Kuerten seized command in the third, grabbing a 3-0 lead and denying Schuettler any chance to rally.
Agassi came from 3-1 down to win the first-set tiebreak, hitting a forehand winner off Kuerten's short service return.
The semi-final between Gustavo Kuerten and Michael Chang in the Montreal Open recently offered some hope for die-hard fans.
Though one-sided (Mr Kuerten won 6-3, 6-1), the contrasting styles of play and personality made for an intriguing match.
The 27-year-old has split with Alexander Volkov and hired Gustavo Kuerten's former coach Hernan Gumy and fitness trainer Miguel Maseo.
Kuerten's return to form comes at the tournament where his unhappy run began exactly one year ago with a first-round elimination.
He and Schuettler played for 35 minutes on Saturday before their match was suspended because of rain with Kuerten leading 6-2 0-1.
Philippoussis said his rhythm was off as he blasted 13 aces against Ferreira compared to 22 a day earlier against Gustavo Kuerten.
"(Kuerten's) beaten me twice, in Monte Carlo and Roland Garros, and it would be good to play him in his home, " said Coria.
Kuerten had earlier closed out his match with Schuettler with a backhand return down the line in the eighth game of the third set.
Kuerten will now play Guillermo Coria in the final on Sunday after the unseeded Argentine beat Cecil Mamiit of the United States 7-5 6-2.
Stepanek followed up a fine five-set victory over Gustavo Kuerten at the Australian Open with a 6-4 6-3 triumph over the tournament's top seed.
And Kuerten predicted more Grand Slam success for the 22-year-old Australian.
At Wimbledon, he crashed out in the second round to 5ft 5ins Belgian Olivier Rochus and at the US Open to a resurgent Gustavo Kuerten.
However, the 25-year-old Paraguayan ran out of steam in the last set and was broken in the fourth game as Kuerten closed the match out 6-3.
In-form Agassi, who beat arch rival Pete Sampras on Wednesday, continued in his impressive vein with a 6-4 7-5 victory over third seeded Brazilian Gustavo Kuerten.
Agassi, who defeated Kuerten in the semi-finals last year, triumphed again but he did not have it his own way in a 7-6 3-6 6-4 win.
Experts on the surface, such as reigning French Open champion Gustavo Kuerten, hold their racket differently to the likes of Tim Henman and Sampras to cope with it.
On his day, the left-hander can beat the best in the world, as 10 Tour titles and victories in 2001 over Pete Sampras, Andre Agassi and Gustavo Kuerten testify.
The most intriguing name continually flying around is that of Larri Passos, who won Grand Slams with Gustavo Kuerten and has watched many Murray matches over the past year.
But it is unclear whether he can he be persuaded to return to the same hotels, practice courts and tournaments as those he visited for 15 years with Kuerten.
"If he maintains a level like this, he will be one of the guys to compare with Andre (Agassi) and Pete (Sampras) with tournament wins and grand slams, " said Kuerten.
He was firmly on course for gold after qualifying for the final round as joint-leader with Ireland's Jessica Kuerten, who also suffered in her last jump by picking up 21 penalties.
That led many experts to tip Ferrero to steal Kuerten's French Open crown, but the Brazilian was in unstoppable form when the pair met in the semi-final for the second straight year.
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