Austrian Thiem produced the surprise of the opening round by knocking out Jarkko Nieminen, and he also put the Wimbledon champion through his paces before ultimately being beaten in the deciding set.
Marin Cilic awaits Murray in the quarter-finals after the Zagreb Open champion eliminated Jo-Wilfried Tsonga in straight sets on Wednesday.
Top seed Juan Martin Del Potro beat Paul-Henri Mathieu 6-2 7-6 to set up a last-eight encounter with Latvian Ernests Gulbis, who only needed two sets to beat Grigor Dimitrov.
Thomas Berdych is also through and meets Jerzy Janowicz in the quarters.
World Indoor Tournament results
1-Juan Martin Del Potro (Argentina) beat Paul-Henri Mathieu (France) 6-2 7-6(2)
2-Andy Murray (Britain) beat Dominic Thiem (Austria) 6-4 3-6 6-3
3-Tomas Berdych (Czech Republic) beat Nicolas Mahut (France) 6-4 6-3
Philipp Kohlschreiber (Germany) beat 4-Richard Gasquet (France) 7-5 7-5
Jerzy Janowicz (Poland) beat 6-Tommy Haas (Germany) 6-4 6-4
Ernests Gulbis (Latvia) beat 8-Grigor Dimitrov (Bulgaria) 6-4 7-6(3)
Igor Sijsling (Netherlands) beat Michael Berrer (Germany) 6-1 6-2
Memphis International results
Ivo Karlovic (Croatia) beat 2-Feliciano Lopez (Spain) 7-6(2) 6-4
3-Lleyton Hewitt (Australia) beat Marcos Baghdatis (Cyprus) 1-6 6-2 6-0
4-Lu Yen-Hsun (Taiwan) beat Denis Kudla (U.S.) 3-6 6-3 6-3
Alex Kuznetsov (U.S.) beat 8-Mikhail Kukushkin (Kazakhstan) 2-6 6-3 7-6(1)
Buenos Aires Open results
Albert Ramos (Spain) beat Filippo Volandri (Italy) 6-2 6-1
1-David Ferrer (Spain) beat Santiago Giraldo (Colombia) 6-4 7-6(1)
4-Nicolas Almagro (Spain) beat Daniel Gimeno-Traver (Spain) 1-6 7-5 6-4
8-Jeremy Chardy (France) beat Alexandr Dolgopolov (Ukraine) 6-3 3-6 7-6(3)