Playing in the semi-finals for the first time and ranked 64 places lower, Jordan fully deserved their victory over Jurgen Klinsmann's shell-shocked side.
South Korea's talisman Son endured a frustrating night and his country's wait for a first Asian Cup since 1960 goes on.
Jordan had more of the chances and deservedly went ahead soon after the break, Yazan Al-Naimat scoring his third goal of the tournament after South Korea gave the ball away cheaply.
They had been in a losing position in four of their matches in Qatar, but there was no way back this time for the Koreans when Mousa Al-Tamari sliced his way through the South Korean defence 13 minutes later.
South Korea simply could not handle the attacking duo of Naimat and Tamari.
"It means everything to me to be in the final and I hope we can do it in the final," he added, having also set Naimat up for the first goal.
"It's also good to be in the final because it will make everyone speak about my country in France and this is very emotional for me."
South Korea's skipper and Tottenham ace Son stood with his hands on his hips at the final whistle in disbelief and coach Klinsmann said his side could have no complaints.
"I am disappointed, I am angry," said the German.
"We did not exist in the first 20-30 minutes."
Klinsmann had made it his stated goal to reach the final in Qatar. Asked by AFP if he will now quit, he said: "There was a lot of good stuff we saw.
"It is a team that is growing and still needs to develop towards the next World Cup.
"There is a lot of work ahead of us. Apart from that, I am not thinking of anything."
- 'Defend this shirt' -
Jordan were the underdogs -- despite the teams drawing 2-2 in the group phase -- but they shaded an entertaining first half in which they racked up 12 attempts at goal to South Korea's four.
In front of 43,000 at Ahmad bin Ali Stadium, South Korean goalkeeper Jo Hyeon-woo was busy almost from the off, saving from Noor Al-Rawabdeh after good work from Tamari.
Jo kept out a fierce drive from Naimat after the South Korean defence opened up, before Tamari blazed over the bar.
South Korea were awarded a penalty on the half-hour that was overturned after the referee consulted the pitch-side monitor, and Lee Jae-sung pinged a header onto the post.
Naimat went up the other end and slalomed his way through three weak Korean challenges before drawing a close-range stop from Jo.
Jordan took the lead on 53 minutes when Park Yong-woo gave the ball away, Tamari ran towards goal and slipped in Naimat, who popped a cool finish over the advancing Jo.
South Korea could not cope with the rampaging duo and on 66 minutes Tamari drove to the edge of the box before unloading past an exposed Jo.
Jordan's Moroccan coach Hussein Ammouta said his players "delivered a heroic performance".
"What you saw today was the fruition of several years of work," he said.
"We must defend this shirt with everything we've got.
"We are growing more ambitious by the hour."
Iran and Qatar play on Wednesday for the other spot in Saturday's final.