Tsitsipas, seeded eight at Flushing Meadow, has now endured consecutive first-round exits at grand slams following his early departure from Wimbledon.
The 21-year-old was clearly struggling with cramp during a ding-dong encounter on Louis Armstrong.
Yet he put in a serious fight, breaking Rublev to love as he served for the match.
But Rublev, also 21, 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.
World number 43 Rublev, who beat Roger Federer in Cincinnati earlier this month, said: "It was tough conditions for both of us and we played an amazing match.
"He started to cramp, I know what it's like, I was cramping too and tried not to show it. But this is amazing, winning matches like this gives you confidence."
Tsitsipas was penalised for a coaching violation and later in the match 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.
Bautista Agut, seeded 10, lost 3-6 6-1 6-4 3-6 6-3 to Mikhail Kukushkin of Kazakhstan.
John Isner, the 14th seed, beat Spain's Guillermo Garcia-Lopez in straight sets.