The top-seeded Frenchman won the event in 2011 and looked on course for a comfortable passage when he took the first set.
But Austrian Thiem fought back well to level things up before taking the Frenchman to a final set tie-breaker where Tsonga clinched the win.
"I was really poor from the baseline but I served well," said Tsonga, who had 16 aces. "I have played many matches like this so I have the experience. That made the difference. I am not in a good shape, I have to fight to win matches."
Tsonga will take on Robin Haase of the Netherlands for a place in Sunday's final, while second-seeded Tommy Haas of Germany faces Lukas Rosol of Czech Republic in the other semi.
Vienna Open quarter-finals
1-Jo-Wilfried Tsonga (France) beat Dominic Thiem (Austria) 6-4 3-6 7-6(3)
2-Tommy Haas (Germany) beat 5-Radek Stepanek (Czech Republic) 7-6(10) 6-3
Robin Haase (Netherlands) beat 3-Fabio Fognini (Italy) 6-7(4) 6-1 6-1
8-Lukas Rosol (Czech Republic) beat Ruben Bemelmans (Belgium) 6-3 1-6 6
Kremlin Cup men’s quarter-finals
1-Richard Gasquet (France) beat Teymuraz Gabashvili (Russia) 6-3 6-2
Ivo Karlovic (Croatia) beat Karen Khachanov (Russia) 6-4 6-0
Mikhail Kukushkin (Kazakhstan) beat Andrey Golubev (Kazakhstan) 6-4 7-6(4)
2-Andreas Seppi (Italy) beat Edouard Roger-Vasselin (France) 5-2 (Roger-Vasselin retired)
Stockholm Open quarter-finals
6-Benoit Paire (France) beat 2-Milos Raonic (Canada) 7-6(3) 6-3
1-David Ferrer (Spain) beat Fernando Verdasco (Spain)WO
5-Ernests Gulbis (Latvia) beat 3-Jerzy Janowicz (Poland) 7-5 4-6 6-3
7-Grigor Dimitrov (Bulgaria) beat Kenny De Schepper (France) 6-4 6-2