Bublik produced relentless brilliance in a match he dominated for long periods before wrapping up a 5-7, 6-3, 6-2 6-4 win.
His drop shot proved to be the key to victory, as he kept Draper off balance and took advantage of his eagerness to stand a long way behind the baseline.
The No 5 seed didn’t change that approach even though Bublik’s drop shot was doing so much damage, but the truth may be that his opponent played at a level that would have tested anyone.
With his booming serve and his incredible variety confusing his opponent, Bublik was too much for Draper to handle and he didn’t try to hide his frustrations after the match.
“It was a tough match. I didn’t play a good match, but I also didn’t play a bad match,” Draper said.
“I thought he played incredibly well. He didn’t allow me to play my tennis, I don’t think.
“I don’t think I’ve reached my best level this week. Then today just a couple of dips here and there, and he took advantage.
“Usually when you play someone like Alexander, he’s quite up and down with his level, but he was completely locked in.
“It hurts a lot, but I just move on. I’m hurt, and for sure I’m really disappointed. I had an opportunity today, and I missed my opportunity, for sure.
“I struggle to put things in perspective, but I think I am proud of the effort that I’ve done on the clay. I think I’ve really improved.
“I always use the lessons from my losses. I always use the fuel and the hurt to better myself.
“It will take a couple of days probably to get over it, but I will, and I’ll move on and keep on getting better.”
Former British Davis Cup player Mark Petchey gave his verdict on the match to TNT Sports, as he admitted the Brit had the racket taken out of his hand by Bublic.
“When you bring a very versatile game to a clay court with a serve like that you can do untold damage,” said Emma Raducanu’s coach. “And credit to him, he has played some beautiful tennis out there.
“That is not about Jack not playing well. That is about Bublik being the problem he can be on the tennis court.”
Former British No 1 Tim Henman echoed Petchey’s view, as he heap praise on Bublik as he also appeared on the TNT Sports panel.
“It was a tough day at the office and I think where Bublik deserves extra credit is the way he went about it,” said Henman. “Jack was the one who got off to a solid start, they were holding serve comfortably. Jack got that break at the end of the first set. He wins it 7-5 and then he gets the early break in the third set.
“You think wow this is where Jack had the opportunity but I think this is where Bublik showed his resilience. Mark mentioned his skillset. Unbelievable ball striking, his second serve just going for absolutely everything.
“I went out there courtside for a set and a half and the quality of play was magnificent. That is where Bublik deserves enormous credit.”
Bublik was lost for words as he reached a Grand Slam quarter-final for the first time in his career as he held back the tears in his on-court interview.
“Sometimes in life there is only one chance, and I had a feeling that was mine. I couldn’t let it slip. Standing here is the best moment of my life – period,” said Bublik.
“Thank you guys, that was amazing. I’m standing here like I won the thing, but what can I say! I can’t cry here – come on, let me be in peace!
“I still have a match to go, I’m a professional tennis player and I’ve got to get ready.”