Elsewhere, Rafael Nadal is now a set and a break up against South African Kevin Anderson.
Nadal, a nine-time champion at Barcelona, said he "wasn't surprised" by Thiem's first win over Murray in three attempts.
He was a break up and then down by one in the third as both players proved near impossible to shake off, but fourth seed Thiem prevailed to claim his third British scalp of the week after knocking out Kyle Edmund and Dan Evans.
Thiem, who is placed ninth in the world rankings, defeated Yuichi Sugita of Japan 6-1, 6-2 his quarter-final match.
Despite his straight sets win, on a centre court which is named after him, Nadal was far from pleased with his week's work in the Catalan capital where rain has made the conditions heavy. He may have even hit it with the back of the racquet. Zeballos earned two break points in the fourth game of the second set but 14-time grand-slam victor Nadal recovered to hold his serve and wrapped up his victory in 94 minutes, setting up a re-match with Thiem, who beat him past year on clay in the Argentina Open semi-finals.
Turkey gave about 20 minutes notice before Syria strikes
Since the PKK launched its terror campaign in 1984, an estimated 40,000 people in Turkey have died in related violence. Earlier, a report published by Turkey's Hurriyet newspaper said that the Turkish army has a plan in Sinjar.
The momentum swung in the eighth game of the set, though, as Murray broke decisively for a 5-3 lead before seeing it out to level at 1-1.
Thiem started strong, breaking Murray's first two service games before adding a third break en route to taking the first set.
Murray was again in trouble at 4-2 down in the decisive set, and folded when he failed to successfully return Thiem's deep lob on match point.
Andy Murray is set to play Spaniard Feliciano Lopez later this afternoon.
Thiem will be seeking his second title of the year and to add to his eight career titles.