Sorribes Tormo flew through the opening set, winning it in just 24 minutes. The Spaniard never faced a break point and won 26 of the 35 points played against the Ukrainian.
Kostyuk rebounded to take the second set in a similar blowout fashion before grabbing a late break in the deciding set to seal a spot in her maiden WTA Tour-level semifinal.
99th-ranked teenager recovers after first set bagel to nip Sorribes Tormo
The Spaniard was off the mark quickly, breaking to open the match after Kostyuk sent a backhand from deep in the court into the net. An angled lob brought Sorribes Tormo a second break and a forehand error by the Ukrainian sealed the set for the world number 66.
Breaks were exchanged to begin the second set and this time it was Kostyuk who took control, a volley winner giving her a break for the first time in the contest and with it, a 3-1 lead.
After a quick hold, Kostyuk broke sizzled a forehand for a winner to go in front 5-1 and on double set point, she watched as Sorribes Tormo steered a forehand long to level the match at one set apiece.
The deciding set saw six consecutive breaks of serve before Sorribes Tormo finally held to stop the streak. It would be the last game she won as Kostyuk saved a break point to hold, broke the Spaniard and forced a backhand error to claim the final three games.