Agassi beat Russian sixth seed Nikolay Davydenko 6-4 7-6 in their rain-delayed quarter-final.
Croatia's Ivan Ljubicic will be aiming to reach his third final in as many weeks when he takes on fifth-seeded Spaniard Tommy Robredo.
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Still struggling to find his best form, the world number one roared in frustration several times as he tried to find his rhythm.
But with Youzhny also playing well below his best, Federer was able to steer himself to victory.
Fourth-seeded Agassi dominated his contest from the outset, breaking Davydenko to love in the opening game of the match.
Although Davydenko levelled at 3-3 following a forehand error from Agassi, the American regained the advantage in the next game which was enough to decide the first set.
Davydenko again found himself on the back foot as he had to fend of a break point in the third game with a forehand volley.
His reprieve did not last long as he dropped his serve two games later with a double fault.
Although Agassi was broken while serving for the match, he claimed the tiebreak 7-4 to seal victory.