The victory improved Safin's record to 3-4 lifetime against the top-seeded and two-time defending champion.
Davydenko had won this tournament in three of the last four years, but Safin captured the decisive third set by winning 9-of-12 points played on his second serve and did not face a break point.
In the third set, Safin broke Davydenko to gain a 4-3 advantage and went on to victory.
In Friday's other quarterfinals, Russian Igor Kunitsyn topped France's Jeremy Chardy 6-4, 6-2; Fabrice Santoro toppled fellow Frenchman Mathieu, the fourth seed, 6-3, 2-0 when Mathieu retired because of illness; and German Mischa Zverev was a 6-4, 3-6, 7-5 winner against Serbian Viktor Troicki by saving two match points.
In Saturday's semifinals, Safin plays Zverev and Santoro faces Kunitsyn.
2014: The Year in Music [PHOTOS]