The second-seeded Coria lost to Czech Tomas Berdych and fourth-seeded Puerta was defeated by Novak Djokovic of Serbia-Montenegro in second-round action.
Berdych needed just over an hour to dispose of Coria, 6-4, 6-2. The loss could keep Coria out of the season-ending Masters Cup. Only the top eight players in the ATP standings make the field for the event in Shanghai later this month.
Djokovic, who needed to qualify for the event, earned a 6-3, 7-6 (11-9) win over the French Open runner-up Puerta.
Third-seeded Nikolay Davydenko of Russia defeated former champion Greg Rusedski, 6-2, 6-2.