The 26-year-old world number five blazed 50 winners, many of them jaw-dropping backhands, to beat the five-time champion 6-7(5) 6-3 7-6(5) in front of a spellbound O2 arena crowd.
“Probably the best match I ever played,” he said. “It was a real classic and epic match which will happen from time to time at these big tournaments.
Having never got past the group stage in three previous appearances at the tournament, he has now beaten Roger Federer and Novak Djokovic back-to-back to book his place in the semi-finals and appears to be the man in form.
“I did it against Roger, and I did it also today. Probably Novak is the best player in the world right now, so I had to do something outstanding, something unusual, and that’s what I did.
“I know that he can play in a high level, but tonight was just phenomenal,” he said. “He just played very courageous tennis and (was) just smacking the ball. He went for broke.”
Djokovic, who faces a decisive clash with Federer on Thursday with the loser guaranteed an early exit, was generous in his praise of Thiem