Thiem, who did not call up his full potential against Rublew, is in the round of the best four for the second time in a row, in 2019 he was defeated by the Greek Stefanos Tsitsipas in the final.
The group runners-up will be determined by the 20-time Grand Slam winner Rafael Nadal from Spain and Tsitsipas (9:00 p.m. in the live ticker at Eurosport.de).
Alexander Zverev has to defeat world number one Novak Djokovic on Friday to stay in the tournament.
He would meet his buddy Thiem in a new edition of the US Open final in the semifinals.
Zverev back on track: “Every match makes me better”