Clarke trailed 4-2 after the third set at the Royal Artillery Barracks, but then produced scores of 29 in the fourth and 30 in the decider to clinch the victory and move a step closer to a medal.
She said: 'That was incredible. One of the most amazing things I've ever done. It came down to the last three arrows, that's the way to do it. I'm looking forward to more 10s next time. I'm now through to the semis. What better way to celebrate your 30th birthday than shooting here?'
Clarke was joined in the semi-finals by fellow Briton and defending Paralympic champion Danielle Brown, who also came from behind as she saw off Spain's Maria Ruboi Larrion 6-4.
Clarke will now play Stepanida Artakhinova, while Brown faces Marina Lyzhnikova for a place in the final - this after the Russian duo both enjoyed comfortable 6-0 wins in their quarter-finals.
There was more joy for Russia in the men's Individual Recurve - Standing as three of the four semi-final spots were claimed by players from the nation. In an all-Russian semi-final, Oleg Shestakov will play Mikhail Oyun and Timur Tuchinov faces the USA's Eric Bennett.
The women's Individual Recurve - Standing champion from Beijing 2008, Lee Hwa Sook of the Republic of Korea, was another player who needed to recover from a slow start to claim her spot in the last four.
The 46-year-old lost the first two sets to world number one Magali Comte of Switzerland but then won the next three sets to progress.
She said: 'I was nervous from the beginning. I calmed myself down and thought I still have three sets and I could win the game. After I found my correct form I hit 10 points.'
Lee will now face Javzmaa Byambasuren of Mongolia in the semi-finals, after she beat Gao Fangxia of China 6-0, although there was better news for the Chinese as Yan Huilian progressed into the last four to set up a match with Poland's Milena Olszewska - who came back from losing the first two sets to Irina Batorova of Russia to seal her 6-4 victory.
In the quarter-finals of the men's Individual Compound - Open, an all-USA battle between Matt Stutzman and Dugie Denton produced a match of high quality in which the duo both hit eight 10s, with Stutzman scoring 143 out of a possible 150 for his aggregate score for the match and Denton getting 142.
Stutzman will face 52-year-old Spaniard Guillermo Rodriguez Gonzalez, who beat Italy's Alberto Simonelli 6-4, in the semis.
The other semi-final will be between Turkey's Dogan Hanci and Finland's 18-year-old archer Jere Forsberg, who needed just three sets to beat Leos Bartos of the Czech Republic 6-0 after hitting seven 10s out of his nine arrows shot.