But Agassi served two consecutive aces to set up his third match point, and won with a forehand volley off a short return.
Henman had four opportunities to secure the match, but Agassi dug deep, forcing a tie-break and eventually pipping Henman to secure the match 7-5 1-6 7-6 (12-10) in a thrilling finale.
The Oxford-based player made it eight points in a row by holding to love, but at 5-5 handed Agassi the advantage again and the American went on to take the set 7-5.
Schuettler was overwhelmed by Agassi in Melbourne eight months ago but was too strong in Montreal, coming through 2-6 6-2 6-3.
In the decider, Henman moved 5-3 ahead when Agassi thrashed a backhand wide, but the American held to force Henman to serve for the match.
It was not to be but, Instead of following the example of Andre Agassi, who made emotional farewell speeches after bowing out from Wimbledon and the U.S. Open last year, Clijsters was practical as ever.
In the third set, the pair exchanged service games to love but the crucial break came in the seventh game when Agassi claimed a winner off Kuerten's second serve to lead 4-3.
But Gilbert came with a CV that included working with former world number ones Andre Agassi and Andy Roddick.
Federer should move past Agassi next week as the American has pulled pout of the Cincinnati Masters, but the Wimbledon champion admits the heavy summer schedule is a problem.
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.
Andre Agassi closed the gap between himself and Champions Race leader Lleyton Hewitt to just 43 points, but not in the manner he would have hoped for.
But the nine-times grand slam singles champion quickly discovered his touch against Becker, best known for ushering Andre Agassi into retirement at the U.S. Open.
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