The British number four, in the second week of a Grand Slam for the first time, fell to 6-3 3-6 6-3 6-4 defeat against eighth seed Rublev.
But Draper’s performances this week will hopefully point to an upward curve in such a promising career hindered by fitness issues. The 21-year-old has endured an injury-hit year and slipped from a ranking of 38, in January, to outside the top 100.
A shoulder problem saw him miss Wimbledon and also threatened his participation at Flushing Meadows.
Yet despite serving well within himself in a bid to manage the problem, Draper was the only British player to reach the last-16, and he gave combustible Rublev plenty of reasons to vent his spleen in a see-saw contest.
Draper took time to settle as the first set raced away from him; Rublev does not only serve at 125mph but he seems to play at that pace as well.
He then had to save five break points, punctuating the rallies with complaints to the umpire about the air-conditioning under the Louis Armstrong Stadium roof and the net sensor, to stay on serve at 2-1 in the second.
Then, from out of nowhere at 3-2, Draper cracked a backhand winner down the line to end a fierce rally and bring up break point.
Rublev promptly sent down a double-fault, and was visibly furious with himself, as he gifted Draper a 4-2 lead and, consequently, the second set.
With Rublev now the agitated party, Draper took advantage and broke again at the start of the third with a walloping forehand winner, only to follow it up with a poor service game to let his opponent back in.
The momentum was back with Rublev and he won six of the next seven games to motor away with the third set.
Draper had never won a four-set match until he beat Michael Mmoh on Saturday, and his exertions - as well as his lack of court time this year - seemed to have caught up with him in the fourth.
Rublev took advantage of a weary service game to lead 3-2 and, although Draper saved two match points on serve, and another on his opponent’s, he was unable to avoid slipping to defeat in two hours and 45 minutes.
Carlos Alcaraz meanwhile wasted little time in seeing off Matteo Arnaldi to march into the quarter-finals at the US Open. The defending champion and world number one was a comprehensive 6-3 6-3 6-4 winner inside Arthur Ashe Stadium.
British number one Cameron Norrie could be forgiven for thinking he had dodged a bullet after losing to Arnaldi in the previous round. The Italian did manage a break at the start of the third but it was quickly snuffed out as Alcaraz raced to victory in under two hours.
“I think the intensity from the beginning until the last ball pleased me,” said the 20-year-old Wimbledon champion.
“I played a really solid match, less mistakes, I played my game. I’m really happy with the performance.”