Baker, who will play in his first ATP final, is on a 15-match winning streak. He broke Davydenko, a former No. 3, three times in the deciding set.
Baker's streak began with a challenger victory in the U.S., which earned him a wild card into his first French Open. He qualified in Nice and saved a match point in the quarterfinals against Mikhail Kukushkin.
Almagro, who had lost his previous two matches against Simon, hit eight aces and saved all four break points he faced.
Almagro won on indoor clay in Sao Paulo in February and bids for his 12th career title.