In Sunday's final, Davydenko will meet Britain's Greg Rusedski, who dismantled Dominik Hrbaty 6-4, 6-3.
Youzhny, the hero of Russia's 2002 Davis Cup triumph when he came from two sets down to defeat Paul-Henri Mathieu of France in the decisive rubber, was serving for the match at 5-4.
But this time the fifth-seeded Muscovite came up just short as Davydenko saved one match point in that game to turn the tide in his favour. Youzhny saved five match points of his own before his opponent was finally able to wrap up victory on his sixth opportunity after nearly three hours.
"I had cramps, my legs were killing me, I was dying on the court, but somehow I just managed to survive," Davydenko said.
Youzhny said: "I was just really unlucky today. On match point he hits the net cord and the ball falls over right on the line. What can I do?"
Rusedski, who outlasted second-seeded Swede Joachim Johansson in three tough tie-break sets in the quarter-finals, had a much easier time against third-seeded Hrbaty.
The Canadian-born Briton said: "I volleyed very well today and that was the key because he returns very well."
Rusedski, whose father is of Ukrainian descent, said he was looking forward to playing Davydenko, who was born in Ukraine.
Rusedski is trying to get his tennis career on track after battling through injuries and doping charges.
