The 32-year-old, in his first singles quarter-final in over a year following career-saving hip surgery in January, was broken early in both sets.
Murray broke back to force a tie-break when the Austrian was serving for victory at 5-4 in the second set.
But the 26-year-old, who is ranked fifth in the world, dominated the tie-break to secure victory in Beijing.
Murray moved encouragingly freely during an evenly balanced match and produced a number of signature drop shots and volleys.
Thiem will play Russia’s Karen Khachanov in the semi-finals after the 23-year-old beat Italy’s Fabio Fognini 3-6 6-3 6-1.
Murray’s last ATP Tour singles quarter-final appearance was a defeat by Spaniard Fernando Verdasco at the Shenzhen Open in September 2018.
The Scotsman will continue his singles comeback at the Shanghai Open this weekend after accepting a wildcard entry.
He has won the title in Shanghai on three previous occasions – in 2010, 2011 and 2016.