Korea finally emerged victorious in what was the fifth quarter-final meeting between the two regional giants in as many Asian Cups -- putting them 3-2 up in their mini-series and breaking Iran hearts.
Yoon, 20, the K-League young player of the year, struck in injury time at the end of the first period of extra-time, weaving his way across the face of the box then hitting a curler past the keeper and into the bottom corner.
The other semi-final will be between Australia and Uzbekistan, also on Tuesday, as the continent's premier tournament approaches its climax.
South Korea had a decent chance after less than a minute, but Manchester United star Park Ji-Sung, winning his 99th cap, totally missed his volley as his side made the far more confident start.
In Friday's pre-match press conference Korean coach Cho Kwang-Rae said he expected Iran -- under the guidance of former South Korean assistant coach Afshin Ghotbi -- to try and foul his side at every opportunity.
The confident Ghotbi dismissed that saying it was proof Cho was running scared, but Park was nailed twice in the opening 10 minutes, once on the edge of Iran's box, as both sides refused to give an inch.
True to Cho's prediction, Iran were physical, conceding a series of free-kicks as they attempted to nullify the likes of Park and impressive attacking midfielder Koo Ja-Cheol, who scored four times in the group stage.
On 24 minutes Lee Yong-Rae fired just wide, then four minutes later Iran came closest to taking the lead when Korean striker Ji Dong-Won inadvertently flicked a Mohammad Reza Khalatbari free-kick back towards his own goal.
But Jung Sung-Ryong pulled off a fine save, diving left and low to claw the ball out. It would have been harsh on the Koreans, whose quick movement and slick passing had their opponents running in circles at times.
South Korea needed to make all the possession count, while Ghotbi urged more from his anonymous captain Javad Nekounam. The game was passing the Osasuna man by.
The English-speaking Ghotbi decided he had seen enough and at half-time brought on Khosro Heidari to replace Mohammad Nosrati, one defender for another. It was a sign the Iran coach knew his side were struggling.
Yet there was no immediate sign it made any difference, as the Koreans started the second period in front of 7,111 at Qatar Sports Club Stadium much as they had ended the first -- in control but making few clear chances.
The lanky Ji rose highest but could only head straight at Iran keeper Mahdi Rahmati on 63 minutes, then Khalatbari caused mild panic in Korea's box in a rare Iranian raid and moments later Ehsan Haji Safi flashed a drive wide.
Ghotbi threw on striker Masoud Shojai, who also plays in Spain for Osasuna, with 15 mins left, as three-times Asian Cup winners Iran belatedly swung the game in their favour. Cho hauled off the fast-fading Koo for Yoon.
It turned out to be a masterstroke.
The match dragged into extra-time with the game square at 0-0 and neither team really threatening to break the deadlock, before highly rated midfielder Yoon finally prised the two sides apart after 105 minutes of football.