Thiem, who also rallied from a set down to defeat Croatia's Borna Coric on Thursday, won his quarter-final match by performing slightly better than Sock on the big points on Friday night.
Although the American saved seven of the 10 break points he faced during the two-hour, 14-minute contest, a crucial service break in the fifth game of the third set proved to be the decisive blow.
The ultra-fit Austrian player has played 70 matches this year on the Association of Tennis Professionals (ATP) World Tour and has a record of 53-17, just one win shy of Germany's Alexander Zverev, who fell to 54-18 after losing 6-1, 6-2 to Khachanov in Friday quarter-final action.
Sock, meanwhile, has stumbled to a 9-21 match record this season. His ranking has fallen from No. 8 at the start of the year to No. 23 and is sure to fall further after his failure to defend his Paris Masters title.
With the win, Thiem remains on track to book a berth in the elite, season-ending ATP Finals for the third straight year. In fact, the Austrian can clinch a spot in London if Swiss great Roger Federer defeats Japan's Kei Nishikori on Friday night.
(This story has not been edited by Devdiscourse staff and is auto-generated from a syndicated feed.)