Dimitrov served 17 aces and missed two chances to break serve when leading 4-3 in the second set, with Tursunov closing it out in 2 hours, 40 minutes.
Tursunov served 12 aces but also eight double faults. He will will play either fifth-seeded Ivan Ljubicic of Croatia or Kazakhstan's Andrey Golubev.
Sergiy Stakhovsky defeated Illya Marchenko 6-4, 6-3 in an all-Ukrainian match. He will meet either sixth-seeded Jo-Wilfried Tsonga or Benoit Paire, both of France.
Although Stakhovsky dropped serve twice, he broke Marchenko twice in each set.
Defending champion Stakhovsky loses in St. Pete
