The American was leading 6-3, 7-5, 4-1 when Davydenko, who began showing signs of distress early in the second set, decided to quit.
Roddick had been forced to save a set point in the second set but was well on top when the Russian called it a day.
The American will now play the winner of Wednesday night's match between third-seeded Australian Lleyton Hewitt and ninth seed David Nalbandian of Argentina.