World number four Thiem, twice a French Opden runner-up, was beaten in four sets by unseeded Italian Thomas Fabbiano, 6-4 3-6 6-2 6-2.
There were extenuating circumstances for the Austrian, who has been suffering with a virus in the build-up to Flushing Meadows and would not have been expecting to mount a serious challenge.
Tsitsipas, however, suffered a second consecutive grand slam first-round exit after his early departure at Wimbledon.
His Russian opponent, Andrey Rublev, had beaten Roger Federer earlier this month and was once again in inspired form, as the two 21-year-olds played out a ding-dong encounter on Louis Armstrong.
Despite struggling with cramp Tsitsipas put up a serious fight, breaking Rublev to love as he served for the match.
But Rublev was not to be denied and broke straight back before holding his nerve and his serve to wrap up a breathless 6-4 6-7 (5) 7-6 (9) 7-5 win.
Tsitsipas did not leave quietly, though. He was penalised for a coaching violation, and later a time violation, and was overheard saying to umpire Damien Dumusois "you're all weirdos".
He was unrepentant afterwards, claiming Dumusois has something against him: "The chair umpire was very incorrect in what he was telling me during the match," Tsitsipas said.
"I don't know what this chair umpire has in specific against my team but he's been complaining and telling me that my team talks all of the time when I'm out on the court playing.
"He's very... I don't know. I believe he's not right, because I never hear anything of what my team says from the outside. And there is nothing that I personally believe can help my game or make me play better.
"My father, who usually does the talking, he's trying to pump me up by saying, you know, 'come on'.
"Raising my confidence by not coaching but by trying to boost me up. I believe the coach for my opponent does the same thing, which is normal.
"This chair umpire, I don't know, he has something against me. I don't know why."
Wimbledon semi-finalist Roberto Bautista Agut was another seed to bite the dust after a gruelling five-setter.
Agut, seeded 10, lost 3-6 6-1 6-4 3-6 6-3 to Mikhail Kukushkin of Kazakhstan.
Ninth seed Karen Khachanov also fell by the wayside, Vasek Pospisil running out a 4-6 7-5 7-5 4-6 6-3 winner, and 18th seed Felix Auger Aliassime lost the all-Canadian affair against Denis Shapovalov in straight sets.
Predictably there was no such trouble for second seed Rafael Nadal, a straight-sets winner over Australian John Millman in a little over two hours.
The Spaniard said: "There were some tough points, his movement is great and it was a match I gave a lot of respect to.
"Always at the beginning everything is a bit new, not easy, so I think I played a good match. More mistakes than usual with the forehand but I'm happy with how I started."