I'm surprised that Fed fans don't seem to think that knocking off Sampras in 01 was a turning point. Even though it didn't happen immediately, I thought he came away from that win with the belief that he really belonged on top.
It was an important win, no doubt about it. Fed was asked about the match that he thought was the turning point in his career and he did mention that match. But for me the lull and inconsistency that followed after that big win is what makes me think otherwise. He had awful losses in the first rounds of Slams the following year when he was one of the favourites to win them. He was still a head case faltering against much lower ranked opponents until he got his act together late 2003.
Maybe it was the most important match in terms of mental strength. If I remember correctly, Federer saved all match points against Agassi playing on the full risk. Maybe he learned then how to deal with TB pressure and his tie-break record overall is so extremely stunning.
Yes, it was a match where he held his nerve and delivered under pressure. One of the best FH's of the match saved for saving MP, and that shot on his own MP wasn't bad either.