Djokovic dispatched Alexander Zverev 7-5, 6-2, 6-2. Thiem bounced Karen Khachanov 6-2, 6-4, 6-2. Djokovic and Thiem will now face off in the semifinals.
"I'm now in the semifinals for the fourth time," Thiem told reporters. "It's incredibly difficult to win a Grand Slam, especially for us players who haven't won one yet, because if everything goes quite normal, we have to beat two players with 15 or more Grand Slams.
"But I will step on the court tomorrow, try everything, of course, give everything. I hope it's going to be positive in the end, but the challenge is huge. Novak is in very good shape again, probably playing the best tennis of his life. I'm in the semi-finals with maybe the three best players of all time, so everybody can see how tough the way it is for me."
Djokovic -- the No. 1 men's player in the world -- is 6-2 against Thiem. The Serbian star has split his two matches against Thiem at Roland-Garros. Thiem had back-to-back wins against Djokovic before losing to him in May at the Madrid Open in Spain. He beat Djokovic in the quarterfinals of the 2017 French Open, winning in straight sets.
Thiem's quarterfinals match lasted 1:47 on Thursday on Court Suzanne-Lenglen. The 2018 French Open runner-up had 24 winners and had just 11 unforced errors in the victory.
Djokovic beat Zverev in 2:09 on Court Philippe-Chatrier. The Serbian went up 1-0 in the first set, but Zverev wouldn't go down easily. The German climbed back for a 5-4 advantage before Djokovic won the final three points of the set. Djokovic dominated the second set, taking a 3-0 lead before Zverev could claim a point.
The duo fought in another tight third set working to a 2-2 score, before Djokovic won the final four points to win in straight sets. Zverev had 40 unforced errors compared to Djokovic's 18 unforced errors.
Djokovic takes on Thiem at 8:50 p.m. Friday at Roland-Garros.