Newly-crowned US Open champion Thiem needed five sets to overcome Hugo Gaston in a fourth-round epic, and it was a marathon once more as the third seed lost to Argentine Schwartzman 7-6 (7-1) 5-7 6-7 (6-8) 7-6 (7-5) 6-2 in a match lasting five hours.
Rafael Nadal now potentially awaits in the last four, with the 'King of Clay' facing Jannik Sinner in his quarter-final tie later on Tuesday night.
After a thoroughly competitive start, it was Thiem who made the first breakthrough, though not without controversy. The Austrian appeared to clip the line as he pushed the 12th seed's drop shot cross-court, and though the umpire agreed, a furious Schwartzman certainly didn't.
Schwartzman wasted no time in hitting back, however, breaking immediately following an error-strewn Thiem service game, before stunning the Austrian in the eventual tie-break, taking it by seven points to one.
Thiem typically responded in true champion fashion, sealing a break in the first game of the second set. However, as with the first set, the world No3 was unable to take advantage of the break, with Schwartzman relinquishing his lead in the sixth game.
And at 4-4, Schwartzman saved six break points in a mammoth 15-minute hold of serve, with a weary Thiem seemingly in trouble as he served to stay in the set.
But Thiem was certainly not done there. He found inspiration from within to hold his serve, before Schwartzman somewhat capitulated to hand the Austrian a break in the following game, which Thiem then pounced on to take the set 7-5.
Thiem once again looked as if he'd got off to the dream start in the third set, but he was quickly penned back despite breaking in the opening game, with Schwartzman sealing back-to-back breaks to move 3-1 up.
The breaks weren't done there, however. In fact, there were a total of eight breaks of serve in a quite remarkable set, which had to be settled in a quintessentially unpredictable tie-break.
Schwartzman somehow fought his way back from 5-1 down, but Thiem again found championship form when needed to take it 8-6.
However, Schwartzman showed his battling spirit again to take the next tie-break and fourth a deciding fifth set, which saw Thiem's understandable tiredness as his serve began to slow noticeably as the two friends still duelled it out across every bit of clay on Philippe-Chatrier.
The crucial moment came in game number six, when Thiem fired into the net twice as Schwartzman sealed a pivotal break and then held comfortable before breaking again to seal an unforgettable win.