Thiem led Andujar by two sets to love but suffered a first opening-round loss in Paris.
Thiem has struggled for form since winning his first grand slam title at the US Open last summer but looked to be finding a way past Andujar when he opened up a two-set lead.
However Andujar, who beat Roger Federer in Geneva last week, fought back to win 4-6 5-7 6-3 6-4 6-4 and record his first victory over a top-five player at the age of 35.
Thiem took a six-week break in March and April to step back from the demands of the tour and bubble life and must now reflect on a first opening-round loss at Roland Garros.
The 27-year-old, who was seeded fourth, has reached at least the quarter-finals on his previous five visits, losing to Rafael Nadal in the final in 2018 and 2019.
Thiem also lost meekly to Britain’s Cameron Norrie in Lyon last week and he was baffled by his performance, saying: “I was not struggling at all with my motivation but the game was just not there today.
“All the shots are missing power. They are not accurate enough. I’m moving not well enough, so everything in my game, there are some percentages missing. I don’t really know why, because since I stepped back on court it’s already two months, and I was really practising well, super intense as well.
“Shots were there in practice and it got also better in Madrid and Rome. But Lyon and here, the shots and all how I moved and everything was just not the real me, I would say, or my version who is able to play for big titles. It’s just not good enough at the moment. And it’s a very tough situation.”
Having fought so hard to win a slam title, Thiem is not the first player to find what comes next a good deal more tricky.
“It’s amazing to reach such a big goal but, at the same time, something is different after,” he said. “It’s a big learning process and, despite the loss, which hurts so much, I still hope I can bounce back stronger than before. But right now I don’t know when the moment is coming.”
Zverev has often taken the scenic route at Roland Garros and he did so again, coming from two sets down to beat fellow German Oscar Otte 3-6 3-6 6-2 6-2 6-0. Qualifier Otte caught Zverev cold but the sixth seed finished strongly to set up a second-round clash with Roman Safiullin.
With Novak Djokovic, Nadal and Roger Federer all being placed in the top half, it is a golden chance for players in the bottom half to reach the final, and Zverev admitted Thiem’s loss affected him.
“I think it did have a little impact on me at the beginning of the match because, yes, you try to focus on yourself, you try to not pay too much attention, but you do know the draw,” he said.
“You know who is where. You know that Dominic is one of the best clay-court players, especially here, one of the toughest opponents you can have, and then he’s out. Maybe that was part of the reason why I was a little bit nervous in the beginning. I’m happy to be through. That’s all that matters for me right now.”
Fifth seed Stefanos Tsitsipas is probably the favourite to make it through from the bottom half and he saved a set point in the opening set before beating France’s Jeremy Chardy 7-6 (6) 6-3 6-1 in a match played without fans because of Paris’ 9pm curfew.
Elsewhere, there were wins for Roberto Bautista Agut, Pablo Carreno Busta, Karen Khachanov and Fabio Fognini but Grigor Dimitrov is out after being forced to retire with a back problem after having match points against Marcos Giron.