Thiem downed the world No 1 6-2, 3-6, 7-5, 5-7, 7-5 to set up a repeat of last year's final against 11-time winner and defending champion Rafael Nadal.
Djokovic, who was second best to Thiem when it came to mastering the gloom, wind and damp of Paris, was bidding to join Rod Laver in the Grand Slam history books.
"When you're playing in hurricane kind of conditions, it's hard to perform your best," said an angry Djokovic.
"It's really just kind of surviving in these kind of conditions and trying to hold your serve and play one ball more than your opponent in the court.
"That's what it felt like playing yesterday. I don't want to point out some reasons or find excuses for this loss. I mean, he took it, he won it, and well done to him."
The match had been controversially suspended on Friday night with the match at one set each but with Thiem up 3-1 in the third and with all the momentum on his side.
Winds of 80km/h were forecast for the evening.
Asked to describe the conditions, Djokovic added: "One of the worst conditions I have ever been part of. That's all I can tell you."
Thiem's coach Nicolas Massu said he would prefer the final to be shifted to Monday but the Austrian insisted he was happy to play Sunday.
That would mean he will have played four days in succession after his quarter-final against Karen Khachanov was put back a day to Thursday after a washout on Wednesday.
Nadal played his last-eight match against Kei Nishikori on Tuesday and completed his straight sets semi-final win over Roger Federer by the middle of Friday afternoon.
"I think it's fine. I mean, it's not the first time that that happens in tennis, and it's not going to be the last time. That's our sport," said Thiem.
Thiem, bidding to become just Austria's second Roland Garros men's champion after Thomas Muster in 1995, said he had no problems stopping for the night on Friday.
"I was not unhappy yesterday, because I went to the locker room with 3-1 lead in the third set.
"The conditions were very, very tough yesterday. I think I never played in such a wind. It was supposed to rain. So, for me, it was a decent decision to interrupt."
But Massu continued to insist it would be fairer to both men if the championship match was played on Monday.
"I asked the referee if it's possible to play on Monday. And they said there is no chance," said the Chilean.
"If you ask me, of course I prefer that Dominic have one day off. He was playing the last four days in a row.
"The other part of the draw play only one match in four days. So they are not in the same situation."
For Djokovic, meanwhile, it was a desperate end to his hopes of reaching a fifth Roland Garros final and 25th at the majors.
On Friday night, he had called the supervisor onto the court to complain about having to play in the high winds.
On Saturday, the 2016 champion's mood was not improved by being slapped with a code violation for unsportsmanlike conduct.
"When the supervisor came on the court, he said as long as there are no flying objects coming on to the court, we're good," fumed Djokovic.
"I didn't know that an umbrella is not a flying object, which flew in in the first game of the match, but that's their decision.
"I guess they know tennis better."