The Czech Republic archer, the gold medallist from the Beijing 2008 Games and one of the big favourites for gold heading into London 2012, found himself 4-0 down to Italy’s Fabio Azzolini after the opening two sets and still trailed 5-1 after the third.
But Drahoninsky showed his class to score 28 out of a possible 30 in the next two sets to take the match into a deciding shoot-off, where the Czech ace scored nine as Azzolini could only manage six with his arrow.
'When I was 4-0 down (after the second set) I said to myself, "David, you must to better",' said Drahoninsky. 'Fabio is a guy who can take advantage of me being under pressure as defending champion, but I managed to pull it round. I expected it to be a tough match, which it proved (to be) but I didn't expect it this tough.'
Drahoninsky will now face Osmo Kinnunen in the semi-finals, this after the 59-year-old held his nerve in the last two sets to beat fellow Finnish archer Jean-Pierre Antonios 6-4.
The other semi-final will be between Jeff Fabry of the USA and Norbert Murphy of Canada. Fabry hit seven 10s on his way to a 7-1 win over Great Britain's John Cavanagh, while Murphy was a comfortable 6-0 winner over Peter Kinik of Slovakia.
In the women’s Individual Recurve - W1/W2, Italy enjoyed fine success in the quarter-finals as Elizabetta Mijno and Veronica Floreno were both victorious.
Floreno saw off Hatice Bayar of Turkey 6-2, while Mijno won by the same score against Turkey's Ozlem Hacer Kalay.
The other two semi-final deciders, meanwhile, provided plenty of drama. Zahra Nemati of Iran caused the biggest shock of the day as she saw off defending champion Gizem Girismen, also of Turkey, 6-0 to set up a clash against Floreno, while China's Li Jinzhi came through a tense shoot-off against Marketa Sidkova of the Czech Republic 6-5.
A good day for the Italian team was completed when Oscar de Pellegrin saw off Lee Myeong-Gu of the Republic of Korea 6-4 to qualify for the last four of the men's Individual Recurve - W1/W2. He will now face Tseng Lung Hui for a place in the final, after the archer from Chinese Taipei saw off Britain's Paul Browne 6-4 in his quarter-final clash.
Ebrahim Ranjbarkivaj saw off fellow Iranian Roham Shahabipour 7-1 to set up a semi-final with Malaysia's Hasihin Sanawi - a 6-4 winner over Jung Young Joo of the Republic of Korea.
Elsewhere at the Royal Artillery Barracks, both the men's and women's Individual Recurve Standing events reached the end of the round of 16.
In the men's competition, Russia saw three of their competitors progress as Oleg Shestakov, Mikhail Oyun and Timur Tuchinov all tasted victory to reach the quarter-finals.
Lee Hwa Sook moved successfully through to the quarter-finals of the women's event as the defending champion from the Republic of Korea won 6-0 against Anna Tzika of Greece, while Poland's Milena Olszewska also impressed in a 7-1 success against Britain's Leigh Walmsley.