The 23-year-old entered the tournament as a wildcard ranked 114, with only two grand slam victories to his name and never having won a five-set match.
Now he has won two in a row, both from seemingly hopeless positions, after beating former semi-finalist Grigor Dimitrov 7-5 3-6 4-6 6-4 7-6 (10-7) on Monday (Tuesday AEST).
Having trailed Zizou Bergs 4-1 in both the fourth and fifth sets on Saturday, Fery was twice a break down in the fourth here but roused himself magnificently to set up a clash with ninth seed Alex de Minaur's conqueror Flavio Cobolli, who he beat at the Australian Open.
After all the doom and gloom surrounding British tennis to start the fortnight, Fery's run has been quite the plot twist, and the Centre Court crowd roared on their new hero.
His victory makes him the first British wildcard to reach the quarters at a grand slam in the open era.
When Dimitrov's final backhand hit the net after three hours 55 minutes, Fery looked to his family and team in the stands in disbelief.
"I've no words right now," he said.
"It's incredibly tough to put words to what I've just felt on a tennis court in front of all you guys. The support was phenomenal.
"First time on this court, five sets against an absolute legend of the game. I grew up five minutes from here, I grew up coming to watch matches on this court."
This was the first time in grand slam history that two wildcards had met so late in a tournament, with Dimitrov having slumped to 146 in the rankings after the cruel injury at the same stage here last year that robbed him of a likely victory over eventual champion Jannik Sinner.
Fery failed to win a point in Dimitrov's first four service games, but broke his next to clinch the opening set.
Dimitrov won the next two sets and seemed in control as he led by a break in the fourth, but he tightened up and allowed Fery to force a fifth.
That went to a tiebreak in which Fery seized his opportunity.
Sixth seed Taylor Fritz is also in the last eight after taming mercurial Kazakh Alexander Bublik.
The American dominated a first-set tiebreak after a battle of high-quality serving and was clinical at the key moments after that to win 7-6 (7-1) 6-4 6-4.
Fritz, whose only appearance in a grand slam final ended in defeat at the 2024 US Open to Sinner, will face either Alexander Zverev or Jiri Lehecka next.
Second-seeded Zverev will have to return on Tuesday to complete the job. The German was up 6-4 7-5 3-3 when play had to be stopped minutes ahead of the 11pm curfew in place for the Championships.
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